  $\beta$-TeVO$_4$ is a frustrated spin 1/2 zig-zag chain system,where
spin-density-wave (SDW), vector chiral (VC)and an exotic dynamic spin-stripe
phase compete at low temperatures. Here we use torque magnetometry to study the
anisotropy of these phases in magnetic fields of up to 5 T. Our results show
that the magnetic-field-induced spin reorientation occurs in the SDW and in the
spin stripe phases for $\mu_0 H \geq 2$~T. The observed spin reorientation is a
new element of the anisotropic phase diagram for the field directions in the
$ac$ and $a^*b$ crystallographic planes. The presented results should help
establishing the model of anisotropic magnetic interactions, which are
responsible for the formation of complex magnetic phases in $\beta$-TeVO$_4$
and similar quantum systems.
