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Wave dark matter (DM) represents a class of the most representative DMcandidates. Due to its periodic perturbation to spacetime, the wave DM can bedetected with a galactic interferometer - pulsar timing array (PTA). We performin this Letter a first analysis of applying the $\gamma$-ray PTA to detect thewave DM, with the data of Fermi Large Area Telescope (Fermi-LAT). Despite thelimitation in statistics, the $\gamma$-PTA demonstrates a promising sensitivitypotential for a mass $\sim 10^{-23}-10^{-22}$ eV. We show that the upper limitsnot far from those of the dedicated radio-PTA projects can be achieved.Particularly, we have fulfilled an analysis to cross-correlate the pulsar data,which has been essentially missing so far in real data analysis but is known tobe crucial for identifying the nature of potential signals, with the Fermi-LATdata of two pulsars.

Detecting Stochastic Wave Dark Matter with Fermi-LAT $\gamma$-ray Pulsar Timing Array