The instalment, to air on May 17, will see the former Angel star play a psychologist, reports TV Guide.
Catering only to the rich and powerful, her character comes to the attention of Reese (Jim Caviezel) when she is targeted by one of her clients.
Acker has previously appeared on Once Upon a Time, Alias and Dollhouse.
She has also re-teamed with Angel co-creator Joss Whedon on his new film The Cabin in the Woods.
Person of Interest was picked up for a second season last month, along with 17 other CBS shows.
The series airs on Thursdays at 9/8c on CBS.
> Person of Interest star Taraji P Henson reveals season two hopes
Watch a clip from Person of Interest below: