Gravitational weak lensing probes the underlying mass distribution in clusters of galaxies and is a powerful anchor to observable-mass relations in cluster-based cosmological analyses. The scatter of weak lensing mass estimates is largely due to the orientation of the triaxial mass distribution. In this work, we aim to find an observable tracer of the orientation. Recent observations and results from simulations suggest that the shape of the brightest cluster galaxy (BCG) traces the shape of the underlying dark matter halo. A robust tracer of halo orientation provides a method for improving weak lensing mass estimates. We use simulated data from The Three Hundred Project to test this hypothesis. The Three Hundred Project is a high resolution hydrodynamical re-simulation of 324 galaxy clusters that includes detailed dark matter and baryonic feedback models. We use these simulated clusters to quantify correlations between the projected shapes of luminous matter and total matter as a proxy for observations. We measure the shape of the BCGs from projected stellar density maps and the shapes of the projected dark matter distribution, measured at different radii, and compute the Spearman correlation coefficient between the shape measurements. We find a measurable correlation, Spearman coefficient of Rsp~0.4, between the orientation of the BCG, measured at tighter radii, and the position angle of the dark matter distribution, measured at r500.