Abstract Radial–velocity (RV) planet searches are often polluted by signals caused by gas motion at the star’s surface. Stellar activity can mimic or mask changes in the RVs caused by orbiting planets, resulting in false positives or missed detections. Here we use Gaussian process regression to disentangle the contradictory reports of planets versus rotation artifacts from Kapteyn’s star. To model rotation, we use joint quasiperiodic kernels for the RV and Hα signals, requiring that their periods and correlation timescales be the same. We find that the rotation period of Kapteyn’s star is 125 days, while the characteristic active-region lifetime is 694 days. Adding a planet to the RV model produces a best-fit orbital period of 100 yr, or 10 times the observing time baseline, indicating that the observed RVs are best explained by star rotation only. We also find no significant periodic signals in residual RV data sets constructed by subtracting off realizations of the best-fit rotation model and conclude that both previously reported “planets” are artifacts of the star’s rotation and activity. Our results highlight the pitfalls of using sinusoids to model quasiperiodic rotation signals.