Astronomers do not have a complete picture of the effects of wide-binary companions (semimajor axes greater than 100 au) on the formation and evolution of exoplanets. We investigate these effects using new data from Gaia Early Data Release 3 and the Transiting Exoplanet Survey Satellite mission to characterize wide-binary systems with transiting exoplanets. We identify a sample of 67 systems of transiting exoplanet candidates (with well-determined, edge-on orbital inclinations) that reside in wide visual binary systems. We derive limits on orbital parameters for the wide-binary systems and measure the minimum difference in orbital inclination between the binary and planet orbits. We determine that there is statistically significant difference in the inclination distribution of wide-binary systems with transiting planets compared to a control sample, with the probability that the two distributions are the same being 0.0037. This implies that there is an overabundance of planets in binary systems whose orbits are aligned with those of the binary. The overabundance of aligned systems appears to primarily have semimajor axes less than 700 au. We investigate some effects that could cause the alignment and conclude that a torque caused by a misaligned binary companion on the protoplanetary disk is the most promising explanation.