Why is George Washington winking in one of his portraits? Because his office was in Alexandria, according to civic boosters in the first president's home town.

The drawing of Washington adorns brochures and lapel buttons being distributed widely by the Alexandria Economic Development Program, a joint agency established by the city government and the local Chamber of Commerce two years ago. Since then Director F. Daniel Montague has directed most of his efforts into a campaign to lure trade and professional associations to Alexandria.

The effort has paid off, he says. Since the program was launched, the number of associations with offices in Alexandria has risen from 45 to more than 90. Officials and employes of the 23 organizations that have decided during the last year alone to move to Alexandria will spend $16.6 million annually, most of it in Alexandria, according to the director's estimates.

Another result has been a broadened tax base, said Montague. This year office-commercial new construction, much of it for the associations, is assessed at $94.1 million and accounts for 28.8 percent total tax revenue. By comparison, the figures in 1980 were $21 million in assessment of new office-commercial construction, making up 13.6 percent of total revenue.

Despite recent cutbacks in employes and activities because of the recession, trade and professional groups make up a significant sector of the region's economy. A third of all the estimated 5,800 national trade and professional organizations have offices in the Washington metropolitan area, and an increasing number of these are moving to suburban Maryland and Virginia where rentals and land prices are often cheaper and commuter traffic is less congested. During January and February, the average rent for office space in newly constructed buildings in the District was $28.46 per square feet; for new space in the Maryland and Virginia suburbs the cost was $15.83.

Alexandria's aggressive pursuit of the association business has at times thrust it into competition with neighboring towns and counties, and has narrowed the gap between Alexandria and other suburban jurisdictions in the number of association offices within their borders.

Tom Parker, chief of economic development in Arlington County, said a list compiled last month showed that 115 associations have offices in his county. Among them is the Air Force Association, which recently chose Arlington County for its headquarters after "major competition" between Arlington and Alexandria officials for the organization's business, he said.

Alexandria is closing in on Montgomery County, where the economic development office reports the presence of about 100 associations, and has passed Prince George's, which has about 50. The Prince George's total includes some local associations with membership only in the county, an economic development spokesman said. Fairfax remains the most popular suburban location, with about 200 trade and professional organizations.

The District still holds a commanding lead in number of associations despite the movement of some out of the city, said William K. Barclift, of the American Society of Association Executives. About 1,000 remain in the city, where new and cheaper leasing deals often can be made as a result of the glut in office space.

One of Alexandria's major attractions has been the availability of smaller buildings and cheaper land prices. Organizations that want to own their buildings are attracted by the lower costs, and low-cost financing provided by industrial development bonds.

The American Physical Therapy Association decided to leave its offices at 15th and M streets NW in the District because "we wanted to own our own building," said Royce P. Noland, the executive director. "The size of our office needs were such that it was not economically practical to buy or build in the District. We did not want to go into the real estate business in a big way."

Noland's association bought one of the four buildings that make up a new waterfront complex in Alexandria named Transpotomac Plaza. The Physical Therapists' building has 35,000 square feet in four stories. The association will use 18,000 square feet and has tenants signed up for about half the remaining space, he said.

Other attractions in Alexandria, according to a survey of associations in the city, include the proximity of National Airport and of major government offices in Washington, and the ambience of Old Town.

In the last three months these other trade and professional organizations have taken steps to move to Alexandria:

* The American Society for Personnel Administration, moving its headquarters from Berea, Ohio, broke ground for construction of a 27,000-square-foot building in the 1600 block of North Washington Street.

* The National Mental Health Association broke ground April 8 for its 22,000-square-foot building at the corner of Prince and South Henry streets.

* The National School Boards Association broke ground April 11 for a 50,000-square-foot building on Duke Street near the King Street Metro station.

* The American Chamber of Commerce executives had a "grand opening" May 1 in their new offices in the Duke Metro complex.

* The International Bottled Water Association had opening ceremonies May 18 in its new offices in a commercial rowhouse development on North Henry street.

* The National Society of Professional Engineers has planned ground breaking May 23 for a 60,000-square-foot building at the corner of King and Peyton streets.

On the front line of Alexandria's sales push has been consultant Jenny Cooper, who personally called on the chief executives of 500 associations in the metropolitan area to invite them to lunch with Mayor Charles E. Beatley Jr. and other city government leaders. Ninety-seven of them came to six luncheons in the last six months, and 10 are "active prospects" for relocating in Alexandria, Montague said.

"A lot of the people I met with were saying the cost is just out of sight in the District. Or they said, our rent's just been increased. And having a Washington address didn't seem to mean that much anymore," said Cooper. Many executives were not interested in moving beyond Alexandria because they "needed to be close to the (Capitol) Hill, or to their members or other associations they dealt with."

Cooper is still making follow-up phone calls to the associations, and says she may make another round of visits next fall.