From the second edition (1989):

a representation of the colloq. or vulgar pronunciation of (have) got a or (have) got to (see get v. 24).

1924 J. Buchan Three Hostages xviii. 263 He‥went forward as if to take her arm. ‘You gotta come along,’ I heard. 1929 E. W. Springs Above Bright Blue Sky 176 ‘That oughta be easy,’ the sergeant suggested. ‘You gotta couple of new pilots that could crash an ice wagon on a prairie.’ 1932 T. S. Eliot Sweeney Agonistes 29 But I've gotta use words when I talk to you. 1955 M. Hastings Cork & Serpent xiv. 210, I gotta little present for you. 1968 A. Diment Gt. Spy Race iii. 35 Sorry, can't stay, gotta rush.