We observed Betelgeuse using ALMA's extended configuration in band 7 (f approximate to 340 GHz, lambda approximate to 0.88 mm), resulting in a very high angular resolution of 18 mas. Using a solid body rotation model of the (SiO)-Si-28(upsilon = 2, J = 8-7) line emission, we show that the supergiant is rotating with a projected equatorial velocity of upsilon(eq) sin i = 5.47 +/- 0.25 km s(-1) at the equivalent continuum angular radius R-star = 29.50 +/- 0.14 mas. This corresponds to an angular rotation velocity of omega sin i = (5.6 +/- 1.3) x 10(-9) rad s(-1). The position angle of its north pole is PA = 48.0 +/- 3.5 degrees. The rotation period of Betelgeuse is estimated to P/sin i = 36 +/- 8 years. The combination of our velocity measurement with previous observations in the ultraviolet shows that the chromosphere is co-rotating with the star up to a radius of approximate to 10 au (45 mas or 1.5x the ALMA continuum radius). The coincidence of the position angle of the polar axis of Betelgeuse with that of the major ALMA continuum hot spot, a molecular plume, and a partial dust shell (from previous observations) suggests that focused mass loss is currently taking place in the polar region of the star. We propose that this hot spot corresponds to the location of a particularly strong "rogue" convection cell, which emits a focused molecular plume that subsequently condenses into dust at a few stellar radii. Rogue convection cells therefore appear to be an important factor shaping the anisotropic mass loss of red supergiants.