Green’s Dictionary of Slang

(US) to sign one’s name.

1968		J. Colebrook Cross of Lassitude 105: Baby, you’re going back to Wentworth jus’ as soon as that judge can John Hancock the papers.
1984		E.M. Rauch Adventures of Buckaroo Banzai [film script] Just John Hancock this, sir [HDAS].