Rotation modulation of Kepler light curves in mid-A to late-B stars is shown to be present. This is demonstrated by the high correlation of projected rotational velocities with photometric frequencies in 30 stars. The time-frequency diagrams show stochastic variations in all respects similar to those in spotted cool stars. This disposes of any explanation in terms of binary proximity effects. More than half of the sample of stars with effective temperatures in the range of 8300-12000K show rotational modulation, indicating that starspots are the rule rather than the exception among A stars. The periodograms of a subset of these stars show a characteristic pattern in which a broad peak is flanked by a sharp peak at a slightly higher frequency. It is demonstrated that the sharp peak has the same width as the spectral window, indicating a stable period over the duration of the 4-yr Kepler observations. It is speculated that this might be a signature of a reflection effect in a non-transiting planet. These observations suggest that the presence of localized magnetic fields in A and B stars and that current views of radiative stellar envelopes need to be revised.