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WISE J224607.56$-$052634.9 (W2246-0526) is a hyperluminous ($L_{\rm bol}\approx 1.7\times 10^{14}~L_\odot$), dust-obscured and radio-quiet quasar at redshift $z=4.6$. It plays a key role in probing the transition stage between dusty starbursts and unobscured quasars in the co-evolution of galaxies and supermassive black holes (SMBHs). To search for the evidence of the jet activity launched by the SMBH in W2246-0526, we performed very long baseline interferometry (VLBI) observations of its radio counterpart with the European VLBI Network (EVN) plus the enhanced Multi Element Remotely Linked Interferometer Network (e-MERLIN) at 1.66 GHz and the Very Long Baseline Array (VLBA) at 1.44 and 1.66 GHz. The deep EVN plus e-MERLIN observations detect a compact (size $\leq32$ pc) sub-mJy component contributing about ten percent of its total flux density, which spatially coincides with the peak of dust continuum and [C II] emissions. Together with its relatively high brightness temperature ($\geq8\times10^{6}$ K), we interpret the component as a consequence of non-thermal radio activity powered by the central SMBH, which likely originates from a stationary jet base. The resolved-out radio emission possibly come from a diffuse jet, quasar-driven winds, or both, while the contribution by star formation activity is negligible. Moreover, we propose an updated geometry structure of its multi-wavelength active nucleus and shed light on the radio quasar selection bias towards the blazars at $z>4$.