Tuning the optical dispersion or topology of iso-frequency contours (IFC) in photonic/plasmonic structures poses an important challenge and has been addressed until now with complex assemblies of multilayer metal-dielectric stacks based metamaterials. In this work, we demonstrate electrostatically tunable photonic dispersion for intraband transitions in multilayer black phosphorus (BP) by experimentally measuring the complex dielectric function below the optical gap along the two principle axes (armchair and zigzag) of BP as a function of carrier density. The underlying mechanism of the tunable optical dispersion stems from the Fermi level-dependent susceptibility of the free-carrier Drude response, whereas the anisotropy comes from the difference in the fermionic masses arising due to asymmetry in the band-structure. Our results show that BP is a promising system to actively access different optical topologies (such as elliptical and hyperbolic) in the mid to far-infrared.