We present a novel approach for assessing the muon content of inclined air showers based on a combined analysis of the radio emission and particle footprint. We will use the radiation energy reconstructed by the Auger Engineering Radio Array (AERA) as an energy estimator and estimate the muon number independently with the water-Cherenkov detector array (WCD) of the Pierre Auger Observatory. We focus our analysis on air showers with primary energy above 4 EeV to ensure full efficiency of the WCD with a grid spacing of 1500 m. Over approximately six years of data, we identify a set of 31 high-quality events that are used in the analysis. The estimated muon content in data is compatible with the one for an iron primary as predicted by current-generation hadronic interaction models. This result can be interpreted as a deficit of muons in simulations as a lighter mass composition is expected from 𝑋max measurements. Such a muon deficit was already observed in previous analyses of the Auger Collaboration and is now confirmed for the first time with radio data.