Moire engineering as a configuration method to twist van der Waals materials has delivered a series of advances in electronics, magnetics and optics. Yet these advances stem from peculiar moire superlattices which form at small specific twisting angles. Here we report the configuration of nanoscale light-matter waves-the polaritons-by twisting stacked $alpha$-phase molybdenum trioxide $alpha$-MoO3 slabs in the broad range of 0$^o$ to 90$^o$. Our combined experimental and theoretical results reveal a variety of polariton wavefront geometry and topological transitions via the twisting. The polariton twisting configuration is attributed to the electromagnetic interaction of highly anisotropic hyperbolic polaritons in stacked $alpha$-MoO3 slabs. The nano-polaritons demonstrated in twisted $alpha$-MoO3 hold the promise as tailored nano-light for on-demand nanophotonic functionalities.
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