  Azimuthal asymmetry of vector-meson production in single-transversely
polarized proton-proton collisions ($p\up p$) is calculated in the string model
of particle production. The asymmetry is generated only during fragmentation of
a high-energy quark into hadrons. The obtained asymmetry of the $\rho^\pm$ is
opposite in sign to that of $\pi^\pm$ mesons. On the other hand, an asymmetry
appearing during parton scattering would contribute with the same sign to that
of vector and pseudoscalar mesons. Thus, a combined measurement of both can be
used to estimate the contribution to the asymmetry from parton scattering.
