Fast Fourier transform of a dataset with nonconstant sampling rate

Is it possible to get the power series of some data that was sampled at an uneven rate? I'm trying to obtain the period of a noisy oscillatory signal generated by a Gillespie simulation. Timesteps using the Gillespie algorithm come from a Poisson distribution, ie they aren't constant.

Can the fast fourier transform work with this type of data or do I need a constant sampling rate?

edit: I should add that this is related to a problem I posted to r/matlab

In case anyone's interested, I ended up using pawnzeeknee's suggestion, which was to use MATLAB's filtfilt command to apply a Butterworth filter without phase shift.