We study the present-day connection between galaxy morphology and angular momentum using the {sc Dark Sage} semi-analytic model of galaxy formation. For galaxies between $ 10^{11}-10^{12} mathrm{M}_{odot}$ in stellar mass, the model successfully predicts the observed trend whereby galaxies with more prominent disks exhibit higher {em stellar} disk specific angular momentum ($j_{rm stellar, disk}$) at fixed stellar mass. However, when we include the gas in the disk, bulge-dominated galaxies have the highest {em total} disk specific angular momentum ($j_{rm total, disk}$). We attribute this to a large contribution from an extended disk of cold gas in typical bulge-dominated galaxies. We find the relationship between $j_{rm dark matter}$ and morphology to be quite complex. Surprisingly, in this stellar mass range, not only do bulge-dominated galaxies tend to live in halos with higher $j_{rm dark matter}$ than disk-dominated galaxies, but intermediate galaxies (those with roughly equal fractions of bulge and disk mass) have the lowest $j_{rm dark matter}$ of all. Yet, when controlling for halo mass, rather than stellar mass, the relationship between $j_{rm dark matter}$ and morphology vanishes. Based on these results, halo mass rather than angular momentum is the main driver of the predicted morphology sequence at high masses. In fact, in our stellar mass range, disk-dominated galaxies live in dark matter halos that are roughly 1/10th the mass of their bulge-dominated counterparts.