Fluctuations can drive continuous phase transitions between two distinct ordered phases — so-called deconfined quantum critical points (DQCPs) — which lie beyond the Landau-Ginzburg-Wilson paradigm. Despite several theoretical predictions over the past decades, experimental evidence of DQCPs remains elusive. We show that a DQCP can be explored in a system of Rydberg atoms arranged on a triangular lattice and coupled through van der Waals interactions. Specifically, we investigate the nature of the phase transition between two ordered phases at 1/3 and 2/3 Rydberg excitation density, which were recently probed experimentally in [P. Scholl et al., Nature 595, 233 (2021)]. Using a field-theoretical analysis, we predict both the critical exponents for infinitely long cylinders of increasing circumference and the emergence of a conformal field theory near criticality showing an enlarged U(1) symmetry — a signature of DQCPs — and confirm these predictions numerically. Finally, we extend these results to ladder geometries and show how the emergent U(1) symmetry could be probed experimentally using finite tweezer arrays.