Context. The study of stellar activity is important because it can provide new constraints for dynamo models when combined with surface rotation rates and the depth of the convection zone. We know that the dynamo mechanism, which is believed to be the main process that rules the magnetic cycle of solar-like stars, results from the interaction between (differential) rotation, convection, and magnetic field. The Kepler mission has already been collecting data for a large number of stars during four years allowing us to investigate magnetic stellar cycles. Aims: We investigated the Kepler light curves to look for magnetic activity or even hints of magnetic activity cycles. Based on the photometric data we also looked for new magnetic indexes to characterise the magnetic activity of the stars. Methods: We selected a sample of 22 solar-like F stars that have a rotation period shorter than 12 days. We performed a time-frequency analysis using the Morlet wavelet yielding a magnetic proxy for our sample of stars. We computed the magnetic index Sph as the standard deviation of the whole time series and the index ⟨ Sph ⟩, which is the mean of standard deviations measured in subseries of length five times the rotation period of the star. We defined new indicators, such as the contrast between high and low activity, to take into account the fact that complete magnetic cycles are not observed for all the stars. We also inferred the Rossby number of the stars and studied their stellar background. Results: This analysis shows different types of behaviour in the 22 F stars. Two stars show behaviour very similar to magnetic activity cycles. Five stars show long-lived spots or active regions suggesting the existence of active longitudes. Two stars in our sample seem to have a decreasing or increasing trend in the temporal variation of the magnetic proxies. Finally, the last group of stars shows magnetic activity (with the presence of spots) but no sign of cycle. Appendix A is available in electronic fom at http://www.aanda.org