We experimentally demonstrate the possibility of quasi-adiabatic conversion of LP11 modes to vortex modes in a twisted highly birefringent fiber with a gradually increasing twist rate. Based on the value of the effective indices, the LP11 modes are selectively converted to right- and left-handed circularly polarized vortex modes HE21 with a total angular momentum of ±2 and to quasi-TE01/TM01 modes with a total angular momentum of 0. Since the proposed conversion method has a purely topological origin, it is broadband in nature, in contrast to the methods based on resonant effects.