It has been argued that measurement-induced collapses in Orthodox Quantum Mechanics generates an intrinsic (or built-in) quantum arrow of time. In this paper, I critically assess this proposal. I begin by distinguishing between an intrinsic and non- intrinsic arrow of time. After presenting the proposal of a collapse-based arrow of time in some detail, I argue, first, that any quantum arrow of time in Orthodox Quantum Mechanics is non-intrinsic since it depends on external information about the measurement context, and second, that it cannot be global, but just local. I complement these arguments by assessing some criticisms and considerations about the implementation of time reversal in contexts wherein measurement-induced collapses work. I conclude that the quantum arrow of time delivered by Orthodox Quantum Mechanics is much weaker than usually thought.