President Reagan has nominated Washington attorney Thomas Penfield Jackson to a seat on the U.S. District Court here vacated last November by Judge Oliver Gasch.

Jackson, 45, who is president-elect of the 4,500-member Bar Association of the District of Columbia, has been in private practice for 18 years in the firm of Jackson, Campbell & Parkinson. He has been a partner in that firm for 14 years.

President James Bierbower of the District of Columbia Bar praised the choice yesterday, saying that "lawyers in the city will welcome him as an experienced trial lawyer, one of their own." Jackson, well known in local bar circles, was praised by several other area lawyers as well.

Jackson, who received his undergraduate degree at Dartmouth and his law degree at Harvard, said yesterday that he is scheduled to be installed June 8 as president of the Bar Association of the District of Columbia, and will assume the presidency pending his confirmation by the Senate to the court seat.

Although most observers said yesterday they had no doubt he would be confirmed, Jackson said he would not want to assume that until the Senate had acted. If confirmed, Jackson would have to resign from the bar office.

Jackson had been considered last year for a seat on both the D.C. Superior Court and the D.C. Court of Appeals, but the city's judicial nominating commission did not select him as a finalist.

That decision caused an uproar within the legal community. Critics of the commission bitterly accused it of rejecting Jackson because he is prominent in Republican circles and because he is a member of the Chevy Chase Club, which has no black members.

Jackson is perhaps best known for his work as a lawyer for President Nixon's Finance Committee to Reelect the President. He defended the committee against a suit brought by Common Cause, which was seeking the names of all campaign contributors. That suit eventually was settled with Common Cause getting the names of many contributors, Jackson said.

If Jackson is confirmed, there would be one vacancy left on the 15-member federal bench. Court sources say that seat, vacated last January when Judge William B. Bryant assumed senior status, is likely to be filled by Chevy Chase lawyer Thomas Hogan.