Transverse momentum spectra of charged particles are measured by the CMS experiment at the CERN LHC in pPb collisions at $$\sqrt{s_{_\mathrm {NN}}} =5.02$$ $$\,\text {TeV}$$ , in the range $$0.4 < p_{\mathrm {T}} < 120$$ $${\,\text {GeV/}c}$$ and pseudorapidity $$|\eta _\textsc {cm} | < 1.8$$ in the proton–nucleon center-of-mass frame. For $$p_{\mathrm {T}} <10$$ $${\,\text {GeV/}c}$$ , the charged-particle production is asymmetric about $$\eta _\textsc {cm} = 0$$ , with smaller yield observed in the direction of the proton beam, qualitatively consistent with expectations from shadowing in nuclear parton distribution functions (nPDF). A pp reference spectrum at $$\sqrt{s}=5.02$$ $$\,\text {TeV}$$ is obtained by interpolation from previous measurements at higher and lower center-of-mass energies. The $$p_{\mathrm {T}}$$ distribution measured in pPb collisions shows an enhancement of charged particles with $$p_{\mathrm {T}} >20$$ $${\,\text {GeV/}c}$$ compared to expectations from the pp reference. The enhancement is larger than predicted by perturbative quantum chromodynamics calculations that include antishadowing modifications of nPDFs.