The stockpile, already more than two pounds of cheese for every person in the United States, is still growing. ''At a time when American families are under increasing financial pressure, their Government cannot sit by and watch millions of pounds of food turn to waste,'' Mr. Reagan said in a written statement.

Participating states would have to distribute the cheese through nonprofit organizations. People would not lose food stamps as a consequence of accepting the cheese, the White House said. California will be the first state to receive some of the cheese, taking delivery Monday of three million pounds of cheddar from storage facilities in that state.

The new farm law seeks to curtail the Government's influence in farm economics, but supporters called it inadequate and critics labeled it disastrous for some farmers and too generous for others. The bill passed the House, 205 to 203, last Wednesday with 59 Republicans voting no.

In Congressional debate, farm state members from both parties said the measure would bankrupt or impoverish many farmers, and consumer interests condemned provisions aiding peanut and sugar farmers. The law will cost the Government at least $3 billion more than the President's original proposal, but about $5 billion less than the measure first passed by the House in October. Legislative Victory for President

Its approval represented a legislative victory for Mr. Reagan even though it continues grain and cotton subsidies and peanut marketing quotas, which the Administration originally opposed.