  We study the two-dimensional magnetohydrodynamics system forced by space-time
white noise. Due to a lack of an explicit invariant measure, the approach of Da
Prato and Debussche (2002, J. Funct. Anal., \textbf{196}, pp. 180--210) on the
Navier-Stokes equations does not seem to fit. We follow instead the approach of
Hairer and Rosati (2023, arXiv:2301.11059 [math.PR]), take advantage of the
structure of Maxwell's equation, such as anti-symmetry, to find an appropriate
paracontrolled ansatz and many crucial cancellations, and prove the
global-in-time existence and uniqueness of its solution.
