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.