Inclusion Criteria:

* Participants must have been previously treated with 1 biologic agent for psoriatic arthritis (PsA) or psoriasis and the reason for discontinuation must be documented
* Have a diagnosis of psoriatic arthritis (PsA) for at least 3 months before the first administration of study intervention and meet classification criteria for Psoriatic Arthritis (CASPAR) at screening
* Have active PsA as defined by: (a) At least 3 swollen joints and at least 3 tender joints at screening and at baseline (b) C-reactive protein (CRP) greater than or equal to (>=) 0.1 milligrams per deciliter (mg/dL) at screening from the central laboratory.
* Have at least 1 of the PsA subsets: distal interphalangeal joint involvement, polyarticular arthritis with absence of rheumatoid nodules, arthritis mutilans, asymmetric peripheral arthritis, or spondylitis with peripheral arthritis
* Have active plaque psoriasis with at least one psoriatic plaque of >= 2 cm diameter or nail changes consistent with psoriasis
* A female participant of childbearing potential must have a negative highly sensitive serum pregnancy test (Beta-hCG) at screening and a negative urine pregnancy test at Week 0 prior to administration of study intervention

Exclusion Criteria:

* Has a history or current signs or symptoms of severe, progressive, or uncontrolled renal, hepatic, cardiac, vascular, pulmonary, gastrointestinal, endocrine, neurologic, hematologic, rheumatologic (with the exception of PsA), psychiatric, genitourinary, or metabolic disturbances
* Currently has a malignancy or has a history of malignancy within 5 years prior to screening
* Has known allergies, hypersensitivity, or intolerance to icotrokinra or its excipients
* Has other inflammatory diseases that might confound the evaluations of benefit of icotrokinra therapy, including but not limited to rheumatoid arthritis (RA), systemic lupus erythematosus, or Lyme disease
* Participants with fibromyalgia or osteoarthritis symptoms that, in the investigator's opinion, would have potential to interfere with efficacy assessments