We present two-dimensional line-of-sight stellar kinematics of the lens galaxy in the Einstein Cross, obtained with the GEMINI 8 m telescope, using the GMOS integral-field spectrograph. The stellar kinematics extend to a radius of 4″ (with 0.″2 spaxels), covering about two-thirds of the effective (or half-light) radius Re - 6″ of this early-type spiral galaxy at redshift zl ≃ 0.04, of which the bulge is lensing a background quasar at redshift zs ≃ 1.7. The velocity map shows regular rotation up to ∼100 km s-1 around the minor axis of the bulge, consistent with axisymmetry. The velocity dispersion map shows a weak gradient increasing toward a central (R < 1″) value of σ0 = 170 ± 9 km s-1. We deproject the observed surface brightness from Hubble Space Telescope imaging to obtain a realistic luminosity density of the lens galaxy, which in turn is used to build axisymmetric dynamical models that fit the observed kinematic maps. We also construct a gravitational lens model that accurately fits the positions and relative fluxes of the four quasar images. We combine these independent constraints from stellar dynamics and gravitational lensing to study the total mass distribution in the inner parts of the lens galaxy. We find that the resulting luminous and total mass distribution are nearly identical around the Einstein radius Re = 0″.89, with a slope that is close to isothermal, but which becomes shallower toward the center if indeed mass follows light. The dynamical model fits to the observed kinematic maps result in a total mass-to-light ratio γdyn = 3.7 ± 0.5 γ⊙,I (in the I band). This is consistent with the Einstein mass Me = 1.54 × 1010 M⊙ divided by the (projected) luminosity within Re, which yields a total mass-to-light ratio of γE = 3.4 γ⊙,I, with an error of at most a few percent. We estimate from stellar population model fits to colors of the lens galaxy a stellar mass-to-light ratio γ* from 2.8 to 4.1 γ⊙,I. Although a constant dark matter fraction of 20% is not excluded, dark matter may play no significant role in the bulge of this ∼L* early-type spiral galaxy.