Solvent vapor annealing is a promising, flexible platform for controlling the self-assembly of block copolymer thin films. However, the ability for static solvent annealing alone to provide sufficient bias to generate vertically oriented features is limited. Here, we use dynamical field theory simulations to investigate the morphology dynamics and capacity for pattern selection of a cyclic solvent annealing process. We find that the swell step selectively strains features oriented parallel to the substrate, reducing their stability with respect to disorder, while vertically oriented domains remain stable through the full cycle. This memory effect may be exploited to systematically improve feature orientation with wide operating margins and favorable kinetics compared to static solvent or cyclic thermal annealing. In aggregate, these results suggest a simple, robust method for orienting features in solvent annealed block copolymer films, potentially obviating the need for external fields while minimizing the total annealing time.