We report the observation of a linear magnetoresistance in single crystals and epitaxial thin films of the pyrochlore iridate Bi$_2$Ir$_2$O$_7$. The linear magnetoresistance is positive and isotropic at low temperatures, without any sign of saturation up to 35 Tesla. As temperature increases, the linear field dependence gradually evolves to a quadratic field dependence. The temperature and field dependence of magnetoresistance of Bi$_2$Ir$_2$O$_7$ bears strikingly resemblance to the scale invariant magnetoresistance observed in the strange metal phase in high Tc cuprates. However, the residual resistivity of Bi$_2$Ir$_2$O$_7$ is more than two orders of magnitude higher than the curpates. Our results suggest that the correlation between linear magnetoresistance and quantum fluctuations may exist beyond high temperature superconductors.
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