Inclusion Criteria:

• 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 >= 1 of the following PsA subsets: distal interphalangeal joint involvement, polyarticular arthritis with absence of rheumatoid nodules, asymmetric peripheral arthritis, or spondylitis with peripheral arthritis
• Have active plaque psoriasis with at least one psoriatic plaque of >= 2 centimeter (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 nonplaque form of psoriasis (for example, erythrodermic, guttate, or pustular)
• Has a history or current signs or symptoms of severe, progressive, or uncontrolled renal, hepatic, cardiac, vascular, pulmonary, gastrointestinal, endocrine, neurologic, hematologic, rheumatologic (except PsA), psychiatric, genitourinary, or metabolic disturbances
• Has suspected or known allergies, hypersensitivity, or intolerance to JNJ-88545223 or excipients used in the investigational medicinal product (IMP), including placebo (JNJ-88545223 investigator's brochure); or has a history of severe allergic reaction, angioedema, or anaphylaxis to drugs or food
• Has fibromyalgia or osteoarthritis symptoms that, in the opinion of the investigator, would have potential to interfere with efficacy assessments
• Currently has a malignancy or has a history of malignancy within 5 years prior to screening