We have measured the intrinsic disk ellipticity for 7 nearby, nearly face-on spiral galaxies by combining Densepak integral-field spectroscopy with I-band imaging from the WIYN telescope. Initially assuming an axisymmetric model, we determine kinematic inclinations and position angles from H-alpha velocity fields, and photometric axis ratios and position angles from imaging data. We interpret the observed disparities between kinematic and photometric disk parameters in terms of an intrinsic non-zero ellipticity. The mean ellipticity of our sample is 0.05. If the majority of disk galaxies have such intrinsic axis ratios, this would account for roughly 50% of the scatter in the Tully-Fisher relation. This result, in turn, places tighter constraints on other sources of scatter in this relation, the most astrophysically compelling of which is galaxy mass-to-light ratios.