We demonstrate an optical recirculating delay loop by shifting the spatial mode order of orbital-angular-momentum (OAM) beams in the free-space. The desired delay can be selected at the loop output by exploiting the orthogonality of the OAM modes. When sending a 20-Gbaud quadrature-phase-shift-keyed (QPSK) signal through the delay system, three recirculations are demonstrated, each with an additional delay of 2.2 ns. Around 0.5 and 2 dB system penalties are measured for the second and third recirculations, respectively. We also simulate the performance of our approach under different scenarios.