  We present a measurement of inclusive $J/\psi$ production at mid-rapidity
($|y|<1$) in $p+p$ collisions at a center-of-mass energy of $\sqrt{s}$ = 200
GeV with the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). The
differential production cross section for $J/\psi$ as a function of transverse
momentum ($p_T$) for $0<p_T<14$ GeV/$c$ and the total cross section are
reported and compared to calculations from the color evaporation model and the
non-relativistic Quantum Chromodynamics model. The dependence of $J/\psi$
relative yields in three $p_T$ intervals on charged-particle multiplicity at
mid-rapidity is measured for the first time in $p+p$ collisions at $\sqrt{s}$ =
200 GeV and compared with that measured at $\sqrt{s}$ = 7 TeV, PYTHIA8 and
EPOS3 Monte Carlo generators, and the Percolation model prediction.
