We present a search for periodicities (Pchr) in the chromospheric Ca ii infrared triplet emission of several stars (τ Boo, 51 Peg, υ And, ρ1 Cnc, ρ CrB, 70 Vir and GL 876) which may be directly attributable to interaction with close‐in giant planets. Activity enhancements could arise from increased non‐radiative heating and dynamo action in planet‐induced tidal bulges (with Pchr≈Porb/2), or from interactions between the stellar and planetary magnetic fields (with Pchr≈Porb). We compare both Pchr and the phase dependence of the activity with the planetary orbital period Porb, the orbital phase, and models. No significant Pchr or phase dependence attributable to planets can be clearly identified. We place approximate upper limits on the amplitude of any planet‐induced activity. We identify a possible stellar rotation period for GL 876, and support previous period determinations for four other stars. We discuss the results and possible directions of future research.