Multiple-input multiple-output (MIMO) systems using Rydberg atomic (RA) receivers face significant scalability challenges in signal detection due to their nonlinear signal models. This letter proposes phase-rotated symbol spreading (PRSS), which transmits each symbol across two consecutive time slots with an optimal π/2 phase offset. PRSS enables reconstruction of an effective linear signal model while maintaining spectral efficiency and facilitating the use of conventional RF-MIMO detection algorithms. Simulation results demonstrate that PRSS achieves greater than 2.5 dB and 10 dB bit error rate improvements compared to current single-transmission methods when employing optimal exhaustive search and low-complexity sub-optimal detection methods, respectively.