We introduce a model for the randomization of complex networks with geometric structure. The geometric randomization (GR) model assumes a homogeneous distribution of the nodes in a hidden similarity space and uses rewirings of the links to find configurations that maximize a connection probability akin to that of the popularity-similarity geometric network models. The rewiring preserves exactly the original degree sequence, thus preventing fluctuations in the degree cutoff. The GR model is manifestly simple as it relies upon a single free parameter controlling the clustering of the rewired network, and it does not require the explicit estimation of hidden degree variables. We demonstrate the applicability of GR by implementing it as a null model for the analysis of community structure. As a result, we find that geometric and topological communities detected in real networks are consistent, while topological communities are also detected in randomized counterparts as an effect of structural constraints.