The first 1952 recording of the song was by Joni James. She had seen the sheet music in the Woods Building in Chicago and the lyrics attracted her. She recorded the song in February, 1952, in Chicago and it was released in March on the local Sharp Records label. After she signed to MGM, it was reissued as her second single on that label on August 5, 1952, after Jo Stafford, Patti Page and Dean Martin had covered it. James' version also was issued on M-G-M Records for national distribution. The best-known early 1952 version of the song was recorded after James' recording by Sue Thompson on Mercury's country label as catalog number 6407. It was soon covered by Patti Page, whose version was issued by Mercury as catalog number 5899, with "I Went to Your Wedding" (a bigger Patti Page hit, reaching No 1) on the flip side. It entered the Billboard chart on August 22, 1952, and lasted 12 weeks on the chart, peaking at No. 4.

Answer this question: who sang the original you belong to me? Let's give stream of consciousness first:
The important part for answering this question is: The first 1952 recording of the song was by Joni James.
So, the final answer is Joni James.