  We present a detailed investigation of the properties of the galactic
rotation curves in the Weyl geometric gravity model, in which the gravitational
action is constructed from the square of the Weyl curvature scalar, and of the
strength of the Weyl vector. The theory admits a scalar-vector tensor
representation, obtained by introducing an auxiliary scalar field. By assuming
that the Weyl vector has only a radial component, an exact solution of the
field equations can be obtained, which depends on three integration constants,
and, as compared to the Schwarzschild solution, contains two new terms, linear
and quadratic in the radial coordinate. In the framework of this solution we
obtain the exact general relativistic expression of the tangential velocity of
the massive test particles moving in stable circular orbits in the galactic
halo. We test the theoretical predictions of the model by using 175 galaxies
from the Spitzer Photometry \& Accurate Rotation Curves (SPARC) database. We
fit the theoretical predictions of the rotation curves in conformal gravity
with the SPARC data by using the Multi Start and Global Search methods. In the
total expression of the tangential velocity we also include the effects of the
baryonic matter, and the mass to luminosity ratio. Our results indicate that
the simple solution of the Weyl geometric gravity can successfully account for
the large variety of the rotation curves of the SPARC sample, and provide a
satisfactory description of the particle dynamics in the galactic halos,
without the need of introducing the elusive dark matter particle.
