An apparatus and method for stabilizing a cannula to a vascular structure. The stabilizer includes a ring that circumferentially surrounds the cannula. Three or more struts extend distally from the ring and are outwardly-deflected by a first angle relative to a first axis that is parallel to a lengthwise central axis of the cannula. Each strut includes a contact pad that radially extends from the strut and is distally-deflected by a second angle relative to a second axis that is orthogonal to the first axis. Three or more arms extend proximally from the ring and each arm opposes one of the struts. The arms are inwardly-deflected by a third angle relative to the first axis. The stabilizer is configured to move relative to the cannula until the contact pads engage the vascular structure, causing the arms to engage and resist further movement of the stabilizer relative to the cannula.
