Definition of gotta from the Oxford Advanced Learner's Dictionary

 

gotta

 
BrE BrE//ˈɡɒtə//
 
; NAmE NAmE//ˈɡɑːtə//
 
(informal, non-standard)
 
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the written form of the word some people use to mean ‘(have) got to’ or ‘(have) got a’, which is not considered to be correct He's gotta go. Gotta cigarette? You should not write this form unless you are copying somebody’s speech. More Like This Contractions in non-standard language ‘nother, ain’t, doncha, dunno, ‘em, gonna, gotcha, gotta, innit, wanna, ya, yerSee worksheet.
See the Oxford Advanced American Dictionary entry: gotta