Determine Frequency Content of Variable Rate Signal (Non Uniform Sampling of Signal)
Basically what you have is data which isn't evenly spaced in time.
The conventional way to take care of the is using the Non Uniform Discrete Fourier Transform.

Another approach would be looking at the Fourier Transform as a weighted sum of the signal in time.
Since you know the time shift between the samples you can build the right "Weights" for this kind of sampling.
Once you have the weights, all you need is to calculate the weighted sum for each frequency you're interested in.