An injection port applier is configured to engage an injection port that has integral fasteners that are movable from a non-deployed position to a deployed position. The applier comprises a shaft, a port engagement portion, and a handle. The port engagement portion is includes a fastener deployment member that is operable to move the fasteners to the deployed position. The handle comprises a first handle portion and a second handle portion. The second handle portion is movable distally relative to the first handle portion in order to actuate the fastener deployment member, to thereby move the fasteners to the deployed position. An elongate actuating member couples the second handle portion with the fastener deployment member. One part of the elongate actuating member translates longitudinally in response to the second handle being moved distally; while another part of the elongate actuating member rotates in response to the first portion translating.