Washington's advocate for rights of the homeless Mitch Snyder is taking his show on the road. In September he will be in Santa Barbara, Calif., leading civil disobedience demonstrations against a local ordinance that forbids sleeping outside. Snyder and other protesters from across the country, including the Rev. Jesse Jackson, will be conducting sleep-ins in Santa Barbara, hoping to be arrested and thrown in jail. Snyder and his longtime companion Carol Fennelly, who will fly to Santa Barbara later this month to organize the campaign, believe the ordinance is designed to drive homeless people out of Santa Barbara.

"It is a narrow and mean-spirited law," Snyder said yesterday, "that we must prove to Santa Barbara is not worth the effort and trouble." Snyder is concerned, he said, because Long Beach, Calif., and Philadelphia are considering similar legislation. One ironic twist is that on Sept. 16, in the middle of the planned civil disobedience campaign, Snyder is to be sworn in by Supreme Court Justice Sandra Day O'Connor as a commissioner on the Rev. Martin Luther King Jr. Federal Holiday Commission. Snyder might want to be careful. It's not likely Justice O'Connor would ever administer an oath of office to someone in a jail cell. Out and About

That was Vice President George Bush jogging along the canal above Seven Locks Road yesterday morning. It's not that he was trotting along in his little running shorts trying hard to be inconspicuous. Anyone out in the midmorning sunshine knew something was afoot. The vice president had an entourage of about 10, a motorcycle policeman clearing the way and another motorcycle policeman bringing up the rear. And of course the usual pack of Secret Service agents were jogging along with him, getting in shape whether they wanted to or not . . .

*Washington seems to be more like the tropics this year than in many previous summers. Just like the tropics, there is a sudden rain shower, and then shortly thereafter the sun is shining again. President and Nancy Reagan had a taste of it yesterday when they returned to the White House from their weekend stay at Camp David. They left the helicopter just as the rains began. The president, dressed in jeans and western-style shirt, didn't seem to mind, but the first lady, in dress and high heels, grimaced. If they had only sat in the helicopter for a few minutes, they would have missed the rain . . .

"Shout Up a Morning," the American National Theater musical opening tomorrow at the Eisenhower Theater, is a story about blacks just six years after the Emancipation Proclamation. Some 21 members of the cast and musicians, wanting to offer a special tribute to Abraham Lincoln, who issued the proclamation of freedom, received a permit from the National Park Service and showed up at the Lincoln Memorial yesterday to perform some of the Nat and Cannonball Adderley songs from the show. It wasn't important whether they had much of an audience. They said they just wanted to do it for Lincoln . . .

*Hospital report: Jerry Garcia, lead guitarist of the Grateful Dead, was improving yesterday after waking from a diabetic coma in Marin County General Hospital in Greenbrae, Calif. Band spokesman Dennis McNally said Garcia had been hospitalized for treatment of diabetes, an infection from an abscessed tooth and exhaustion after a tour . . .

Former president Jimmy Carter is scheduled to be at Washington Cathedral this afternoon to eulogize his former commander, retired admiral Hyman Rickover, who died Tuesday at 86. The father of the nuclear Navy, who was abrasive and made his share of enemies, will also be eulogized by Adm. James D. Watkins, the former chief of naval operations, also a submariner. Rickover was buried at Arlington National Cemetery Thursday at a private ceremony attended by his widow Eleonore and a few members of his family. According to a member of the late admiral's staff, it was still uncertain late yesterday afternoon who would be representing the Reagan administration at today's service . . .