This　work　proposes　a　covert　transmission　scheme　for　integrated　sensing　and　communication　(ISAC)　scenario,　where　the　radar　with　the　aid　of　an　intelligent　reflecting　surface　(IRS)　is　employed　to　achieve　covert　communication　and　target　detection　simultaneously.　Specifically,　we　jointly　design　the　transmit　beamforming　vector　of　radar　and　the　phase　shifts　of　the　IRS　to　maximize　the　covert　rate　subject　to　a　covertness　constraint,　a　total　power　constraint,　and　a　detection　mutual　information　constraint.　To　solve　the　non-convex　optimization　problem,　we　resort　to　alternating　optimization　and　the　semidefinite　relaxation　method.　Numerical　results　illustrate　the　effectiveness　of　the　covert　transmission　system　aided　by　the　IRS　and　demonstrate　the　performance　trade-off　between　radar　detection　and　covert　communication.　©　2023　IEEE.