Layered transition metal dichalcogenide WTe$_2$ has recently attracted significant attention due to the discovery of an extremely large magnetoresistance, a predicted type-II Weyl semimetallic state, and the pressure-induced superconducting state. By a careful measurement of the superconducting upper critical fields as a function of the magnetic field angle at a pressure as high as 98.5 kbar, we provide the first detailed examination of the dimensionality of the superconducting condensate in WTe$_2$. Despite the layered crystal structure, the upper critical field exhibits a negligible field anisotropy. The angular dependence of the upper critical field can be satisfactorily described by the anisotropic mass model from 2.2 K ($T/T_csim0.67$) to 0.03 K ($T/T_csim0.01$), with a practically identical anisotropy factor $gammasim1.7$. The temperature dependence of the upper critical field, determined for both $Hperp ab$ and $Hparallel ab$, can be understood by a conventional orbital depairing mechanism. Comparison of the upper critical fields along the two orthogonal field directions results in the same value of $gammasim1.7$, leading to a temperature independent anisotropy factor from near $T_c$ to $<0.01T_c$. Our findings thus identify WTe$_2$ as a nearly isotropic superconductor, with an anisotropy factor among one of the lowest known in superconducting transition metal dichalcogenides.
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