Despite its success at modeling the large-scale structure of the universe, the Lambda Cold Dark Matter (ΛCDM) cosmological model faces some problems on small scales. For small galaxies, ΛCDM simulations with only dark matter predict cuspy central density profiles that rise steeply at small radii, while observed rotation curves of many dark-matter-dominated galaxies imply constant-density cores at their centers. This cusp-core problem may indicate the importance of including baryonic feedback, which effectively rearranges dark matter in the centers of galaxies, but it could also point to a need to reconsider the CDM model and study alternative dark matter models with properties that affect small scales while still looking like ΛCDM on large scales. One such model is self-interacting dark matter (SIDM), which introduces non-gravitational scattering between dark matter particles. My work shows that simulations of dwarf galaxies with SIDM (cross section σ/m = 1 cm^2/g) predict cored density profiles that are distinguishable from baryonic-feedback-induced cores in CDM simulations: the transition between a central core to an outer NFW-like profile occurs more quickly in density profiles of SIDM than in CDM with feedback-induced cores. This difference could potentially help differentiate between CDM and SIDM in observations of dwarf galaxies.