The first results on K^⁎(892)^± resonance production in inelastic pp collisions at LHC energies of s=5.02, 8, and 13 TeV are presented. The K^⁎(892)^± has been reconstructed via its hadronic decay channel K^⁎(892)→±K_S⁰+π^± with the ALICE detector. Measurements of transverse momentum distributions, p_T-integrated yields, and mean transverse momenta for charged K^⁎(892) are found to be consistent with previous ALICE measurements for neutral K^⁎(892) within uncertainties. For p_T>1 GeV/c the K^⁎(892)^± transverse momentum spectra become harder with increasing centre-of-mass energy from 5.02 to 13 TeV, similar to what previously observed for charged kaons and pions. For p_T<1 GeV/c the K^⁎(892)^± yield does not evolve significantly and the abundance of K^⁎(892)^± relative to K is rather independent of the collision energy. The transverse momentum spectra, measured for K^⁎(892)^± at midrapidity in the interval 0 < p_T<15 GeV/c, are not well described by predictions of different versions of PYTHIA 6, PYTHIA 8 and EPOS-LHC event generators. These generators reproduce the measured p_T-integrated K^⁎±/K ratios and describe well the momentum dependence for p_T<2 GeV/c.