Periodic radio bursts from very low mass stars and brown dwarfs simultaneously probe their magnetic and rotational properties. The brown dwarf 2MASSI J1047539+212423 (2M 1047+21) is currently the only T dwarf (T6.5) detected at radio wavelengths. Previous observations of this source with the Arecibo observatory revealed intermittent, 100%-polarized radio pulses similar to those detected from other brown dwarfs, but were unable to constrain a pulse periodicity; previous VLA observations detected quiescent emission a factor of ~100 times fainter than the Arecibo pulses but no additional events. Here we present 14 hours of Very Large Array observations of this object that reveal a series of pulses at ~6 GHz with highly variable profiles, showing that the pulsing behavior evolves on time scales that are both long and short compared to the rotation period. We measure a periodicity of ~1.77 hr and identify it with the rotation period. This is just the sixth rotation period measurement in a late T dwarf, and the first obtained in the radio. We detect a pulse at 10 GHz as well, suggesting that the magnetic field strength of 2M 1047+21 reaches at least 3.6 kG. Although this object is the coolest and most rapidly-rotating radio-detected brown dwarf to date, its properties appear continuous with those of other such objects, suggesting that the generation of strong magnetic fields and radio emission may continue to even cooler objects. Further studies of this kind will help to clarify the relationships between mass, age, rotation, and magnetic activity at and beyond the end of the main sequence, where both theories and observational data are currently scarce. A video of a short talk discussing this work is at http://youtu.be/OqCtFxcBB2s, and an experimental Web-native version of the paper may be viewed at http://purl.org/net/pkgwpub/goreham.