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 2.2ns. Around 0.5 and 2dB system penalties are measured for the second and third recirculations, respectively. We also simulate the performance of our approach under different scenarios.