A bill to keep the troubled Social Security old-age trust fund solvent through 1981 cleared the House Ways and Means Committee by a 19-to-0 vote yesterday.

"We would have to reinstitute the poorhouse if we didn't keep this program sound," declared House Social Security subcommittee chairman J. J. (Jake) Pickle (D-Tex.).

The bill would guarantee that the old-age trust fund has enough money to pay all benefits until the middle or end of 1982, instead of running out of money sometime in 1981.

Pickle said this would give Congress time to undertake a major restructuring of the system in 1981 to put Social Security on a sound long-term financial basis.

Social Security Commissioner William J. Driver endorsed the bill and also said he would oppose any attempts to "roll back" Social Security tax increases already scheduled for Jan. 1, 1981, under previous laws. Even with the bill and the revenues from the previously scheduled increases, he said, the system will be in a different position, and rolling back the scheduled increases would make it "impossible" for it to remain sound.

The bill approved yesterday would not increase Social Security taxes beyond those already scheduled. It simply would divert to the old-age trust fund for two years some money from the financially sound disability insurance fund.

A similar bill has been approved by the Senate Finance Committee.

The current 6.13 percent payroll tax, levied on the first $25,900 of income, will rise to 6.65 percent on the first $29,700 on Jan. 1 under a 1977 law.The maximum tax will thus rise from $1,587 in 1980 to $1,975 in 1981 for the highest-paid workers, but for someone making $10,000 it will go only from $613 to $665.