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Abstract We present X-ray to radio frequency observations of the bright long gamma-ray burst GRB 210702A. Our Atacama Large Millimeter/submillimeter Array 97.5 GHz observations show a significant rebrightening by a factor of ≈2 beginning at 8.2 days post-burst and rising to peak brightness at 18.1 days before declining again. This is the first such rebrightening seen in a millimeter afterglow light curve. A standard forward shock model in a stellar wind circumburst medium can explain most of our X-ray, optical, and millimeter observations prior to the rebrightening, but significantly overpredicts the self-absorbed radio emission, and cannot explain the millimeter rebrightening. We investigate possible explanations for the millimeter rebrightening, and find that energy injection or a reverse shock from a late-time shell collision are plausible causes. Similar to other bursts, our radio data may require alternative scenarios such as a thermal electron population or a structured jet to explain the data. Our observations demonstrate that millimeter light curves can exhibit some of the rich features more commonly seen in optical and X-ray afterglow light curves, motivating further millimeter wavelength studies of GRB afterglows.