Green’s Dictionary of Slang

to make fun of someone; to make a fool of oneself.

1933		J.T. Farrell Gas-House McGinty 63: Don’t let ’em egg you, John.
1965		S. Yurick Warriors (1966) 89: The bitch smiled [...] ‘Some man you are.’ ‘All right,’ the little leader said. ‘Stop egging me.’.
1995		Eble Campus Sl. Apr. 4: egg – act silly, stupid, make a fool of oneself.
1997		S. Armitage ‘Eclipse’ in CloudCuckooLand 117: He was egging himself, I know that.