The object of the invention is to provide an anti-sway stabilizer (20) that is pivotally connected to a support arm (26) of a vehicle bike transportation rack, making available a convenient attachment of a bicycle top tube to the support arm for prevention of a bicycle held on the rack from swaying to and fro when subjected to over the road vehicle movement. The anti-sway stabilizer consists of a rubber bike separator cradle (22) that includes a bore (24) therethrougth that slides over the vehicle bike rack support arm and has a thru-hole (28) parallel with the bore. A pivoting stabilizer member (32) in the form of a yoke (36) is rotatably attached to the bike separator cradle with a screw (40) and nut (42). An attachment strap (48) secures a bicycle top tube to the bike separator cradle and a second attaching strap (48) secures a bicycle seat tube or down tube to the stabilizer member. The anti-sway stabilizer is held in place on the support arm by the combination of the separator cradle being resilient and the rigid stabilizer member contiguously engaging the support arm which precludes any lateral movement along the arm when a force is exerted in a horizontal direction biasing the anti-sway stabilizer.