The Agriculture Department is doubling the fee it charges farmers for grading cotton, in hopes of recovering the full cost of doing the job.

Effective immediately, the fee will rise from 67 cents per bale to $1.15. The government graded cotton free until 1981, when the Reagan administration established a 60-cent fee.

Over the next year, the USDA expects to grade a relatively small crop, 7.9 million bales, for about $8 million. The rest of the $10.5 million cost of the program is expected to be raised by selling cotton samples used in the grading. Cranston Asks Explanation of Transfer

Sen. Alan Cranston (D-Calif.) has asked Clarence Thomas, chairman of the Equal Employment Opportunity Commission, to explain why he ordered an EEOC employe transferred from California to Alabama six months before the employe's retirement.

Frank Quinn, who has directed the EEOC's San Francisco office for 16 years, was transferred to Montgomery, Ala., shortly after being quoted in a Newsweek article as saying a number of his cases had been "spiked" for no apparent reason. Quinn's attorney said that his client was misquoted.

Quinn and Thomas both refused to comment. In a last-minute agreement worked out by Special Counsel K. William O'Connor, the EEOC said it will "temporarily detail" Quinn to his new job for 30 days while O'Connor completes his probe.