The invention discloses a support system for constructing a steel arch bridge by a repeated vertical rotating method. A horizontal connecting bracket consists of two octagonal connecting rods in a horizontal plane and a plurality of first connecting rod systems which integrate the two connecting rods by welding; two anchors are respectively anchored in a mountain and fixedly connected with ends of the connecting rods; two lower steel arch rib hinged supports are respectively hinged with the other ends of the connecting rods and used for connecting lower steel arch ribs; a plurality of lower supports are vertically arranged below the two connecting rods; and upper steel arch rib assembly brackets are arranged above the connecting rods and comprise a plurality of upper supports which are vertical to the connecting rods, and a plurality of second connecting rod systems which integrate the upper supports by welding. The support system has different functions at different construction stages, can bear different loads such as pull, press, bend and the like, has stable and reliable connection and simple construction, and provides safe and quality assurance for the repeated steel arch vertical rotating method.