  We model the effects of the spiral arms of the Milky Way on the disk stellar
kinematics in the Gaia observable space. We also estimate the Gaia capabilities
of detecting the predicted signatures. We use both controlled orbital
integrations in analytic potentials and self-consistent simulations. We
introduce a new strategy, which consists of comparing the stellar kinematics of
symmetric Galactic longitudes (+l and -l), in particular the median transverse
velocity (from parallaxes and proper motions). This approach does not require
the assumption of an axisymmetric model. The typical differences between the
transverse velocity in symmetric longitudes in the models are of ~2 km/s, but
can be larger than 10 km/s for certain longitudes and distances. The kinematic
differences for +l and -l show trends that depend on the properties of spiral
arms. Thus, this method can be used to quantify the importance of the effects
of spiral arms on the orbits of stars in the different disk regions, and to
constrain the location of the arms, main resonances and, thus, pattern speed.
Moreover, the method allows us to test the dynamical nature of the spiral
structure (e.g. grand design versus transient multiple arms). We estimate the
number of stars of each spectral type that Gaia will observe in representative
Galactic longitudes, their errors in distance and transverse velocity, and the
error in computing the median velocity as a function of distance. We will be
able to measure the median transverse velocity with Gaia data, with precision
smaller than ~1 km/s up to distances of ~4-6 kpc for certain giant stars, and
up to ~2-4 kpc and better kinematic precision (<= 0.5 km\s) for certain
sub-giants and dwarfs. These are enough to measure the typical signatures seen
in the models. We also show that a similar strategy can be used with
line-of-sight velocities from other upcoming spectroscopic surveys.(Abridged)
