The parton-level top quark (t) forward-backward asymmetry and the anomalous chromoelectric (d^_t) and chromomagnetic (μ^_t) moments have been measured using LHC pp collisions at a center-of-mass energy of 13 TeV, collected in the CMS detector in a data sample corresponding to an integrated luminosity of 35.9 fb^-1. The linearized variable A⁽¹⁾_FB is used to approximate the asymmetry. Candidate tt^- events decaying to a muon or electron and jets in final states with low and high Lorentz boosts are selected and reconstructed using a fit of the kinematic distributions of the decay products to those expected for tt^- final states. The values found for the parameters are A⁽¹⁾_FB = 0.048^+0.095_-0.087(stat)^+0.020_-0.029(syst), μ^_t = -0.024^+0.013_-0.009(stat)^+0.016_-0.011(syst), and a limit is placed on the magnitude of |d^_t| < 0.03 at 95% confidence level.