Single photon detectors are key for time-correlated photon counting applications [1] and enable a host of emerging optical quantum information technologies [2]. So far, the leading approach for continuous and efficient single-photon detection in the optical domain has been based on semiconductor photodiodes [3]. However, there is a paucity of efficient and continuous single-photon detectors in the microwave regime, because photon energies are four to five orders of magnitude lower therein and conventional photodiodes do not have that sensitivity. Here we tackle this gap and demonstrate how itinerant microwave photons can be efficiently and continuously converted to electrical current in a high-quality, semiconducting nanowire double quantum dot that is resonantly coupled to a cavity. In particular, in our detection scheme, an absorbed photon gives rise to a single electron tunneling event through the double dot, with a conversion efficiency reaching 6 %. Our results pave the way for photodiodes with single-shot microwave photon detection, at the theoretically predicted unit efficiency [4].