How to estimate the autocorrelation from nonuniformly spaced data
As suggested by  Marcus Müller, interpolation in the time domain could be a solution. I never had to perform such a task, and the outcomes may depend in the nonuniformity of your sampling. I propose a use of the Wiener-Khinchin theorem:


  The Fourier transform of the autocorrelation function is the power
  spectrum, or equivalently, the autocorrelation is the inverse Fourier
  transform of the power spectrum


You may use for instance:


a non-uniform DFT (for instance NUFFT),
variants of the Lomb-Scargle periodogram (aka Least-squares spectral analysis),


and get a regularly sampled power spectrum, which I hope you could inverse Fourier back to an estimate of the autocorrelation. As I have no practical experience, if you intend to try this, I'd really appreciate you could share the outcomes, good or bad, along with the specificities of your signal:


what kind of nonuniformity (additive random, jitter, lacunary)?
type of signal and noise?


Additional references:


Power Spectral Density of Unevenly Sampled Data by Least-Square Analysis: Performance and Application to Heart Rate Signals, Laguna et al., 1998
Spectral estimates from nonuniform samples, L. Shaw, 1971