  We calculate the rotational broadening in the observed thermal spectra of
neutron stars spinning at moderate rates in the Hartle-Thorne approximation.
These calculations accurately account for the effects of the second-order
Doppler boosts as well as for the oblate shapes and the quadrupole moments of
the neutron stars. We find that fitting the spectra and inferring the
bolometric fluxes under the assumption that a star is not rotating causes an
underestimate of the inferred fluxes and, thus, radii. The correction depends
on the stellar spin, radius, and observer's inclination. For a 10 km neutron
star spinning at 600 Hz, the rotational correction to the flux is ~1-4%, while
for a 15 km neutron star with the same spin period, the correction ranges from
2% for pole-on sources to 12% for edge-on sources. We calculate the
inclination-averaged corrections to inferred radii as a function of the
neutron-star radius and mass and provide an empirical formula for the
corrections. For realistic neutron star parameters (1.4 M$_\odot$, 12 km, 600
Hz), the stellar radius is on the order of 4% larger than the radius inferred
under the assumption that the star is not spinning.
