  In the present study we are interested in the Sivers effect in process
$p^{\uparrow}p\to DX$. We calculate the transverse single-spin asymmetry (TSSA)
of $D$-meson production within two phenomenological models, namely the
Generalized Parton Model (GPM) and it's Colour Gauge-Invariant formulation
(CGI-GPM), which takes into account the transverse momenta of initial partons.
The last one allows us to study process-independent Sivers functions. To
predict production cross-section of $D$-mesons we use a fragmentation approach
with scale-independent Peterson fragmentation function, taking in mind nonzero
masses of $c$-quark and $D$-mesons. Estimates for the TSSAs, as a function of
transverse momentum and Feynman variable $x_F$ of $D$-meson, within the
conditions of the planned SPD NICA experiment are presented for the first time.
