Yes you can, and even nonuniform time sampling can be beneficial to processing in some cases.
First, have a look at the data: the sampling intervals are shown here:
Quite regular (around 2000 in average), with fluctuation around this value, similar to jitter, except at some locations where you have a huge variations. You should carefully check those, and filter them if you suspect they are not normal. I have more concerns about your signal:
A lot of zeroes, only positive values. Looks like you have absolute values. Traditional vibration signals do not look like that.
Anyway, you can invest in non-uniform DFT, as proposed by @Jojek.
You can have a look at the Lomb-Scargle periodogram or least-squares frequency analysis,
a classic method for finding periodicity in irregularly-sampled data
On your data, you get this, but I would not dare interpret, given the warning above:
Recent matlab versions are for instance
plomb.m, and fast ones exist in Python. MatlabCentral offers at least three implementations: