Attosecond angular streaking (or "attoclock") is an insightful technique for probing the ultrafast electron dynamics in strong laser fields. Up until recently, this technique relied solely on an accurate measurement of the photoelectron momentum distribution and has remained restricted to atomic targets. Here, we propose a novel attosecond angular streaking scheme applicable to molecules, for which the ionic fragments of dissociative ionization are detected in the polarization plane of a close-to-circular polarized laser light. Our ionic attoclock measurements are consistent with theoretical results from a numerical solution of the time-dependent Schrödinger equation and an upper bound of 10 as on the tunneling time from the attoclock readings in the H_{2} molecule has been given, which is significantly smaller than any definitions of tunneling time available in the literatures.