The United States registered a seasonally adjusted $7.03 billion international transactions deficit during last year's fourth quarter, the largest since the government began keeping records in 1920, the Commerce Department said yesterday.

The deficit for the October-December quarter boosted the 1977 total to $20.2 billion, surpassing by far the 1976 deficit of $1.4 billion and more that double the previous record of $9.9 billion recorded in 1972, the department reported.

The fourth-quarter deficit was $2.7 billion above the third-quarter deficit of $4.3 billion, and was the sixth consecutive quarterly deficit, the department said.

The U.S. balance of payments on a current account basis measures trade in goods and services with other nations as well as such unilateral transfers as nonmilitary foreign aid.

Huge deficits in the merchandise trade account - which tracks the volume of exports and imports - have the Carter administration headaches. During 1977, the trade deficit totaled $26.7 billion, topping the previous record of $6.4 billion in 1972.

During the fourth quarter, net receipts for services dropped by $1.6 billion to $2.9 billion. Decreases in transfers under American military agency sales contracts and in direct investment income receipts, and an increase in U.S. investment income payments accounted for most of the decline.

Among capital account transactions, U.S. assets abroad increased by $11.7 billion, which was $7.3 billion more than in the third quarter, largely reflecting a step-up in outflows of funds through U.S. banks to their foreign branches.

Foreign assets in the U.S. increased by $19.1 billion compared with a gain of $13.9 billion in the third quarter, the department said.

The main cause for the huge increase in the international transactions deficit last year was a marked deterioration in the United States global trade account, which showed a deficit of $31.2 billion last year.

But this was offset by an $11 billion surplus in the service account, which includes such things as overseas purchases of U.S. insurance and investment income. This was $2.9 billion higher than the previous year's.

Meanwhile, U.S. assets overseas rose by $26 billion last year compared with a $43 billion increase in 1976.

The slowdown was caused by American banks granting fewer loans abroad and a decline in American purchases of foreign securities.

However, foreign assets in the United States rose sharply in 1977, increasing by slightly more than $49 billion, following a $34 billion increase the previous year.