We present the investigation on deformation of orbital angular momentum (OAM) modes in bending ring-core fibers (RCFs) with different structure sizes through numerical and experimental studies. The effective refractive index differences of even and odd fiber eigenmodes, which constitute OAM±1,1 modes, induced by RCF bending and their impacts on the OAM±1,1 mode intensity distributions are analyzed. Bending experiments are also carried out on three different RCFs, and the results match well with simulation values. It is found that RCFs with smaller inner and outer radii show preferable tolerance to the fiber bending.