A Study to Evaluate the Safety, Tolerability, Pharmacokinetics, and Efficacy of ABBV-3373 in Participants With Moderate to Severe Rheumatoid Arthritis (RA)

* Participant has the clinical diagnosis of RA for \> 3 months based on the 1987 American College of Rheumatology (ACR) classification criteria or 2010 ACR/European League against Rheumatism (EULAR) criteria. * Participant meets the following disease activity criteria: \>= 4 swollen joints (based on 28 joint count) and \>= 4 tender joints (based on 28 joint count) at Screening and Baseline visits and disease activity score (28 joints) (DAS28) C-reactive protein (CRP) \>= 3.2 at Screening. * Participant has an incomplete response to methotrexate. Participants must have been on oral or parental MTX therapy \>= 3 months and on a stable prescription of 15 to 25 mg/week (or \>= 10 mg/week in participants intolerant of MTX at doses \>= 15 mg/week) for \>= 4 weeks prior to the first dose of study drug. Participant must be expected to be able to continue on stable dose of MTX for the duration of study participation.

* Participants previously exposed to adalimumab or other anti-tumor necrosis factor (TNF) biologics. * Participants previously exposed to non-anti-TNF biologics or targeted synthetic disease-modifying antirheumatic drugs (DMARDs) for RA, with exception of participants exposed for less than 3 months and terminated not due to lack of efficacy or intolerability.