Actually, you can use "I sung a song yesterday". According to Leech & Svartvik, the past form allows both "sang" and "sung". However, it is rarely used. (British national corpus returned 96 hits for "he sang" and 2 for "he sung")
SIng sAng sUng a song
Would not have learned OR learnt OR both?
A singer is a person who sings songs.
The singer sang a song yesterday.
The singer has sung many songs since 2007
These type of irregulars that change in all three categories follow alphabetical order in the past tense and participle:
sing sang sung
sink sank sunk
ring rang rung
SING / SANG / SUNG