Recent experiments on magic-angle twisted bilayer graphene have discovered correlated insulating behavior and superconductivity at a fractional filling of an isolated narrow band. Here we show that magic-angle bilayer graphene exhibits another hallmark of strongly correlated systems - a broad regime of T-linear resistivity above a small density-dependent crossover temperature - for a range of fillings near the correlated insulator. This behavior is reminiscent of similar behavior in other strongly correlated systems, often denoted "strange metals," such as cuprates, iron pnictides, ruthenates, and cobaltates, where the observations are at odds with expectations in a weakly interacting Fermi liquid. We also extract a transport "scattering rate," which satisfies a near Planckian form that is universally related to the ratio of (kBT). Our results establish magic-angle bilayer graphene as a highly tunable platform to investigate strange metal behavior, which could shed light on this mysterious ubiquitous phase of correlated matter. © 2020 American Physical Society.