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.