You are essentially referring to nonuniform signal sampling in which data samples are not acquired at exact periods but have same random jitter deviations from their exact uniform timing positions.
Now under some suitable conditions (such as the jitter length being less than a period), there are very effective algorithms which can perfectly convert the nonuniformly sampled data into their equivalent uniform samples. (i.e., given the values of nonuniform samples they give a new set of values which correspond to the perfect uniform samples).
After this nonuiform to uniform conversion, you can then apply the usual FFT, which assumes that the data to be transformed was uniformly sampled.
However, before such a DSP attempt, I would suggest you understand the sampling and read out mechanism of the Arduino Uno and MPU 6050 6DOF sensor combination. That sensor can be read in either a single data read mode or in a burst buffer data read mode. In this second mode, I think it will provide a set of buffered data which are sampled by the MPU6050 unit itself as uniform as possible, compared to a sigle data read mode mastered by the Arduino.
From your data, there seems to be a drift of a few milliseconds per sample. I assume a 20 milli second of sampling period is quite achievable with less than 1 ms of timing accuracy using the Arduino in a proper configuration. So may be your main problem is on the software configuration?
EDIT: Try the following MATLAB code as is:
NOTE: The following code MAY result in WORSE results than available before processing... The success highly depends on the application.
% NONUNIFORM SIGNAL DEFINITION
N=100; % Converts a block of length N nonuniform samples to uniform
M = N*K; %
Tsam = 0.020; % Sampling period in seconds,
% tp represents the nonuniform sampling times
tp = [0:Tsam:(K-1)*Tsam] + Tsam*(rand(1,K)-0.5);
xnunds = sin(2*pi*1*tp); % A simulated nonuniformly sampled data...
% GENERATE THE MATRIX AND ITS INVERSE
A=zeros(K,K); % initial matrix to be inverted
AI=inv(A); % Inverse matrix is here
% APPLY THE CONVERSION FORMULA
xint=zeros(1,K); % interpolate to uniform samples
for m=1:K % per nonuniform sample loop
for q=1:K % calculation of PSI for each m
PSI = PSI + AI(q,m) * sinc( ((n-1)*Tsam/N - tp(q))/Tsam);
ACS=ACS+xnunds(m)*PSI; % acumulation of multiplicant
xint( (n-1)/N + 1)=ACS; % result for each n is assigned
title('nonuniform samples imposed on true samples');
title('interpolated uniform samples imposed on true uniform samples)