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RbEuFe₄As₄ is a stoichiometric compound that undergoes a superconducting transition at T_c = 37 K and a magnetic transition at T_n = 15 K in which Eu-moments order into a type–A antiferromagnetic structure. Thus, an interleaved stacking of ferromagnetic Eu-layers and superconducting Fe₂As₂ layers arises. Using magnetoresistance, magnetization and specific heat measurements we construct the magnetic and superconducting phase diagrams and find that the anisotropy Γ of the upper critical field H_c2 is surprisingly low, Γ ~ 1.8. No re-emergent resistive state associated with the onset of magnetic order is seen below T_c for current flow in or out of plane. The saturation field for the Eu-moments is ~2 kG for in-plane fields and ~20 kG for out-of-plane magnetization, consistent with an in-plane moment orientation. Specific heat measurements reveal that in magnetic fields, magnetic fluctuations become pronounced extending to temperatures well above T_c. We attribute a negative normal-state magnetoresistance for in-plane as well as c-axis currents to scattering by these magnetic fluctuations.