Social Security payroll taxes rose sharply yesterday as the new rates for 1981 came into force. The first paycheck of the new year will contain an unpleasant shock for those who do not follow tax policy closely.

Employes and employers will pay out significantly more in payroll taxes to help cover the growing cost of Social Security payments to retires after yesterday's rise in both the rate of the payroll tax and in the cut-off level of income above which the tax is not levied.

Income up to $29,700 a year ($571 a week) now will be subject to a payroll tax of 6.65 percent. Last year's rate was 6.13 percent levied on income up to $25,900 a year ($498 a week). The maximum amount of Social Security tax paid by any individual thus will rise from $1,588 a year to $1,975 a year.

Without the increase in the payroll tax, legislated as part of the 1977 Social Security Amendments, the Social Security trust fund would soon run out of money to pay retirees checks. Present estimates suggest that still further increases in the tax will be necessary before long if the trust fund is to remain self-financing.

The outgoing adminstration last August proposed, as part of a 1981 tax package, a "refundable" income tax credit -- that is, one that can exceed an individual's total tax liability -- to offset the payroll tax increase. But this would be a step towards financing Social Security payments out of general revenues, rather than out of a specific trust fund, and almost certainly would have been resisted heavily. It runs counter to the philosphy that Social Security is a kind of insurance, rather than a government handout.

The Joint Committee on Taxation has estimated that payroll-tax liability for business and individuals together will go up by about $22 billion this year to $160.6 billion. Not all of this will represent a net gain to federal revenues, however, as businesses pay less in income taxes as a result of increased payroll-tax liabilities, which can be deducted as a business expense.