We present a measurement of the low-energy (0-60 keV) γ-ray spectrum produced in the α decay of ^{233}U using a dedicated cryogenic magnetic microcalorimeter. The energy resolution of ∼10 eV, together with exceptional gain linearity, allows us to determine the energy of the low-lying isomeric state in ^{229}Th using four complementary evaluation schemes. The most precise scheme determines the ^{229}Th isomer energy to be 8.10(17) eV, corresponding to 153.1(32) nm, superseding in precision previous values based on γ spectroscopy, and agreeing with a recent measurement based on internal conversion electrons. We also measure branching ratios of the relevant excited states to be b_{29}=9.3(6)% and b_{42}<0.7%.