The State Finance Committee, nervous about a possible election-day backlash over the new crude-oil tax, voted yesterday to exempt effectively most "small" royalty holders from the levy -- at least for the current year.

By unanimous vote, the panel approved a measure that would grant landowners who lease their property to oil drillers a credit of up to $1,000 against the taxes they owe under the crude-oil levy enacted earlier this year.

The amendment, which amounts to a virtual $1,000 tax exemption for some 500,000 to 2 million individual royalty holders, was designed to quell a burgeoning political backlash in western and southwestern states.

Although many royalty holders are oil companies and other large corporations, millions of oil royalties are held by farmers and other small landowners, who apparently were caught unawares by the tax.

Oil-state senators sought to describe these constituents yesterday as ordinary home-town citizens, some of whom they said are "low-income" persons. Sen. Robert Dole (R-Kans.) complained, "They're paying the same . . . as Exxon."

Dole and Sen. David L. Boren (D-Okla.), who consponsored the tax-relief measure, said complaints from constituents were so numerous that the crude-oil tax had become a major issue among voters in their states.

Sen. Billy Bradley (D-N.J.), skeptical about Dole's descriptions of royalty holders as low-income perons, sought to limit the tax break to landowners with incomes below $30,000, but he was argued down in committee.

Yesterday's measure was tacked onto the committee's "reconciliation" proposal, required by the new congressional budget resolution as a vehicle for raising $4.2 billion in additional revenues to help balance the budget.

Although the royalty-holder proposal would drain $200 million from Treasury revenues, the committee voted to offset this by increasing the portion of the crude-oil tax that applies to large oil companies.

Under the present crude-oil tax law, landowners who allow oil companies to drill on their property in exchange for royalty payments from those firms must pay taxes on a portion of the recent increase in domestic oil prices.

The tax due by royalty holders is collected over the year by the companies that take oil from their land, much as a department store would collect a state sales tax.

Yesterday's Finance Committee measure would allow royalty holders to claim a tax credit of up to $1,000 against the taxes they owe as a result of the crude-oil levy, but only for the 1980 tax year.

Dole has served notice he plans to offer an amendment next year that would exempt all royalty holders whose land yields fewer than 10 barrels a day. The Finance Committee proposal was described as an interim measure.

Yesterday's tax credit would be available only to individual landowners, not to corporations that hold royalties. A royalty is a payment that an oil producer makes to a landowner for the right to drill on his property.

The panel's new tax credit was approved over the objection of the Carter administration, which argued that recent sharp increases in oil prices had left royalty holders "substantially ahead" financially of where they were in 1979.

However, Dole and Boren contended that many royalty holders were simply ordinary man-on-the-street investors whose earnings were slashed sharply by the crude-oil tax.

Finance Committee Chairman Russell B. Long (D-La.) lashed out at Treasury officials for questioning the move, suggesting the administration was putting itself in the position of "taxing people in a poverty area."