The athletic department of the University of the District of Columbia has failed to pay more than $105,000 in grant-in-aid tuition payments for athletes and has not accounted fully for several thousand dollars in ticket sales money from basketball games last spring, according to a report by the D.C. auditor.

The athletic department also has accounted improperly for gifts or donations for its programs and has kept inadequate records of purchases and cash transactions, according to the audit.

The department, which has an annual budget of about $600,000, "does not have adequate internal controls and has not been following sound operating procedures," auditor Otis H. Troupe said in the report released this week.

UDC president Benjamin H. Alexander, who assumed his post in late summer, said in a letter to Troupe accompanying the report that "we concur generally with each of your recommendations" that the school tighten its accounting procedures.

Yesterday, Alexander said only, "I am going to go over this matter with staff . . . we are going to make corrections as needed."

The university's eight-page response attached to the audit said that many accounting standards suggested by the auditor are already required by university rules. Officials pledged to adhere to the standards in the future.

The response also said the university would require the athletic department to keep its tuition payments current for athletes receiving grants-in-aid.

Since the spring of 1980, the department has failed to pay $105,768.41 in tuition for students in its variety of sports programs, according to Donald L. Isaac, an assistant auditor who prepared the report for Troupe.

"The failure to spend these funds as they were budgeted should have been noted and stopped by the budget and accounting staff that monitors the Athletic Department's financial activity," said the report, which criticized both the department and the university for failing to maintain strict accounting procedures.

Former athletic director Orby Moss, who resigned in September to become athletic director of North Carolina A&T University at Greensboro said yesterday that he has not seen the auditor's report.

Moss, in Washington for a football game between his school and Howard University, said his department's financial accounting procedures "were never questioned. . . . We had receipts and proper justification for our expenses."

The audit report said that the athletic department reported ticket sales receipts of $9,700 for the NCAA Division II quarterfinal tournament game against Cheyney State at UDC on March 13.

The report said the auditors were unable to confirm the gross income from ticket sales "because of the failure to properly control the printing and sale of the tickets."

The audit said the comptroller of the university, and not the athletic department, should have had responsibility for the ticket sales. It said that the practice of using cash transactions for supplies "is inconsistent with proper accountability and sound financial practice."

The report also said, "the lack of internal controls . . . results in unreliable data concerning the Athletic Department's financial transactions" and "it does leave the system vunerable to abuse (i.e. kickbacks, skimming, etc.)."

The report said the department's purchases of supplies and services "should be made by check," and that the department should "set forth clear guidelines concerning acceptable documentation" for expenses accounts and advances.