We look for specific correlations predicted by magnetospheric accretion models for young stars that assume disk-locking using stellar and accretion parameters derived from low-resolution HST-STIS spectra of 33 T Tauri stars in the Orion Nebula Cluster. Our results provide strong support for the correlation predicted by a model that does not constrain the stellar magnetic field to a specific geometry, while little support is found for the correlation that assumes a dipolar stellar field geometry. These results support the conclusions from similar studies of older T Tauri stars in Taurus and NGC 2264 and underscore the role that trapped flux plays in regulating a young star’s angular momentum as detailed by Ostriker & Shu. While our targets were all selected to be accreting young stars based on photometric indices, approximately half of the observed stars show no significant signs of accretion in our spectra, illustrating the difficulty in using photometric indices to find accreting stars and the possible role that variability has in the appearance of spectra in young stars. Although values of accretion luminosity derived from our models agree well with those derived from Hβ luminosity for strongly accreting stars, we find that accretion luminosity derived from Hβ luminosity is not a reliable parameter for discriminating between weakly accreting and nonaccreting T Tauri stars due to chromospheric emission that is likely present in all T Tauri stars.