This paper investigates a novel fluid antenna multiple access (FAMA)-assisted wireless powered communication network (WPCN), in which a hybrid access point (HAP) equipped with multiple fixed position antennas (FPAs) provides integrated data and energy transfer (IDET) services towards low-power devices that are equipped with a single fluid antenna (FA), while the low-power devices use harvested energy to power their own uplink transmission. Using the block correlation channel model, both the downlink and uplink wireless data transfer (WDT) outage probabilities are analyzed under specific port selection strategies, including downlink signal-to-interference ratio-based port selection (DSPS) strategy, downlink energy harvesting power-based port selection (DEPS) strategy, uplink signal-to-noise ratio-based port selection (USPS) strategy, and uplink channel-based port selection (UCPS) strategy. A step function approximation (SFA) approach is also relied upon to derive closed-form expressions for the outage probabilities, while the lower bounds for uplink WDT outage probabilities are also formulated. Numerical results demonstrate the validity of our theoretical analysis, which also provide useful guidelines for the system design through the analytical framework.