This paper studies the performance of a wireless powered communication network (WPCN) under the non-orthogonal multiple access (NOMA) scheme, where users take advantage of an emerging fluid antenna system (FAS). More precisely, we consider a scenario where a transmitter is powered by a remote power beacon (PB) to send information to the planar NOMA FAS-equipped users through Rayleigh fading channels. After introducing the distribution of the equivalent channel coefficients to the users, we derive compact analytical expressions for the outage probability (OP) in order to evaluate the system performance. Additionally, we present asymptotic OP in the high signal-to-noise ratio (SNR) regime. Eventually, results reveal that deploying the FAS with only one activated port in NOMA users can significantly enhance the WPCN performance compared with using traditional antenna systems (TAS).