RZ Ari is a fast rotating apparently single M giant of 2.2 Msun. It is fairly evolved to tip RGB or early AGB stage. In addition, the star is known as semi-regular variable. We have studied its longitudinal magnetic field variability using spectropolarimetric data obtained with Narval at Telescope Bernard Lyot, Pic du Midi Observatory, France in the period 2008 - 2018. Two periods were identified using the Lomb - Scargle method: 1310 days and 498 days. The second one is very close to the Long Secondary Period of RZ Ari (480 days) and maybe we observe for first time an interplay of the magnetic field and pulsations for a M giant. Taking into account literature data we determined the radius of the star (117.2 Rsun) that is consistent with the AGB phase. Our work hypothesis is that RZ Ari with its fast rotation is an intermediate case of dynamo generated magnetic field and shock wave compression generated fields as we observe in Miras. These stars are the next evolutionary stage, after early-AGB stars. Further study is required to confirm or reject the hypothesis and to understand better the interplay of the magnetic field and pulsation in this fairly evolved giant.