Green’s Dictionary of Slang

(US) to make pregnant, to impregnate.

1933		S. Walker Night Club Era 148: Winchell and his imitators would write that the couple are ‘preparing a bassinet,’ ‘getting storked’ or awaiting ‘a blessed expense’.
1975		G. Underwood ‘Razorback Sl.’ in AS L:1/2 67: stork vt Make pregnant.
1980		Maledicta IV:2 (Winter) 198: Providing he is wearing a jo-bag she should not be storked.