We present a construction of one-time memories (OTMs) using classical-accessible stateless hardware, building upon the work of Broadbent et al. and Behera et al.. Unlike the aforementioned work, our approach leverages quantum random access codes (QRACs) to encode two classical bits, $b_0$ and $b_1$, into a single qubit state $\mathcal{E}(b_0 b_1)$ where the receiver can retrieve one of the bits with a certain probability of error. To prove soundness, we define a nonconvex optimization problem over POVMs on $\mathbb{C}^2$. This optimization gives an upper bound on the probability of distinguishing bit $b_{1-α}$ given that the probability that the receiver recovers bit $b_α$ is high. Assuming the optimization is sufficiently accurate, we then prove soundness against a polynomial number of classical queries to the hardware.