The catastrophic-care bill awaiting President Reagan's signature will mean the biggest expansion of a federal health program in a quarter century but carries a less-welcome surprise for millions of elderly Americans: a big income tax increase.

For many Medicare recipients, the increase would more than wipe out the gain won when the tax system was overhauled in 1986.The tax increase would kick in for 1989 income for anyone who is eligible for Medicare. It would start by adding 15 percent to regular tax next year, jump to 25 percent in 1990 and then rise by as much as one percentage point a year thereafter, conceivably reaching 35 percent by the end of the century.

This tax increase would pay for about two-thirds of the cost of protecting Medicare recipients against catastrophic hospital, physician and drug expenses; the program would cost an estimated $33 billion over the next five years alone. The remainder of the cost would be covered by raising the monthly Part B premium paid by recipients for doctors' services.

Thus, those who benefit from the expanded program would pay the entire cost - at least for the near future. "We have not asked our children to pay the medical bills that we incur," said Rep. J.J. Pickle, D-Texas. "These benefits will be paid for by the men and women who will use the coverage."

But even some members of Congress who voted for the bill worried aloud that as the tax burden on the elderly grows, pressure will mount to have other taxpayers share the cost.

The compromise bill cleared by Congress last week is considerably more generous than the version recommended by Reagan. Nevertheless, there is no indication that the president will veto it, even with the tax increase.

Sponsors of the bill are reluctant to use the term "tax increase." Rep. Dan Rostenkowski, D-Ill., chairman of the House Ways and Means Committee, repeatedly referred to it as "a new income-related premium."

Negotiators who wrote the final version of the bill decided that paying for the expansion solely by raising the Part B premium would have made it prohibitively expensive for lower-income people.

The final compromise, said Sen. Bob Dole, R-Kan., "takes into consideration an individual's ability to pay for this protection and in doing so allows this coverage to be more affordable for low-income beneficiaries."

Congress estimates the average tax increase will be $285 per person in 1989 and $506 in 1993.

The bill includes several restrictions:

-It would hit only those people eligible for Medicare (enerally age 65 or older or disabled) whose incomes are high enough that they already pay at least $150 income tax. Typically and elderly couple with adjusted gross income of $11,000 or less would not be subject to the increase.

-The maximum tax would be $800 per person in 1989 (1,600 for a couple if both spouses are eligible for Medicare), rising to $1,050 (2,100 per couple) in 1993.

-The tax will be at a rate of $22.50 for each $150 of regular income-tax liability in 1989; by 1993, $42 per $150 of liability.