Frequency of a periodic signal with distortions
The signal looks like narrow band noise and may not be periodic at all.  The FFT will generally reveal a periodic signal that is in the presence of some noise.

In the FFT results, if you have a periodic signal, you should see peaks at the fundamental and its harmonics.  If the "periodic" signal is unstable (modulated in some way) the peaks will become less distinct.

You can try different window functions on your data to see if more defined harmonic peaks become visible in the FFT data.  For example compare results using a number of windows such as Gaussian and Blackman-Harris windows.

Also the choice of the window size (length of data) used when computing the FFT will affect your frequency resolution (bin spacing).  If you can roughly estimate the period of the signal, choose a data length that is a multiple of the estimated period so the bins line up with the signal harmonics.  In general a longer data set will provide better frequency resolution than a shorter data set, so if you don't know the period of the signal, go with a longer data set.