In contrast to all earlier Sonny Boy Williamson records, this one also gained a review in the Cash Box magazine, possibly supported by the regional chart success of "Nine Below Zero". In its September 5, 1953 issue it was featured as the "Rhythm 'N Blues Sleeper O' The Week", suggesting a release some weeks before (not years though). Anyway, at the time of the review publication "I Cross My Heart" had already reached #8 on the Cash Box "Hot in Memphis" regional chart (which it had entered at #10 the week before).
Both sides of this record were recorded on August 5, 1951 in Jackson, MS, together with six other Sonny Boy Williamson sides. The House Rockers were Willie Love (or David Cambell) on piano, the guitars of Elmore James and Joe Willie Wilkins, bass player Leonard Ware and an unknown drummer.
Because of the recording date and the Trumpet catalog number this record is generally listed as a 1951 release (e.g. The Amazing Secret History of Elmore James by Steve Franz, 2003, p. 259: Nov 1951) as it was entered here. Unlike Trumpet No. 139 (released 15 Sep 1951) and No. 145 (released Nov 1951), this one was not advertised in The Billboard magazine in 1951 though, and like No. 140 and No. 168 (both released in 1952) it has the modified artist credit "Sonny Boy Williamson, His Harmonica and House Rockers", instead of just Sonny Boy Williamson.
However, there is no sign that this record was released in 1952 either. In fact, it was reviewed in the Billboard issue of 12 Sep 1953page 41, so it was obviously released in the long span between No. 166 (Feb 1953) and No. 212 (Dec 1953). Considering the usual delay until the publication of the review, I assume an August 1953 release.