The purpose of this study is to assess the efficacy and safety of TAS5315 in combination with methotrexate in a 12 week or 36 week in participants with rheumatoid arthritis with inadequate response to methotrexate.

Inclusion Criteria:

• Have a diagnosis of RA according to 2010 ACR/ EULAR rheumatoid arthritis (RA) classification criteria
• Have been treated with methotrexate (MTX) for at least 90 days prior to screening, and must be on a stable dose between 8 and 16 mg/week for at least 56 days prior to screening.
• Have an inadequate response to MTX
• Have a minimum of 6 swollen and 6 tender joints from 66/68 joint count
• Have hsCRP of ≥ 0.6 mg/dL

Exclusion Criteria:

• Have been treated with conventional synthetic disease-modifying anti-rheumatic drug, except for MTX, within 28 days prior to randomization
• Have an inadequate response to biologic disease-modifying anti-rheumatic drug or Have been treated with 2 biologic treatment
• Have been treated with Janus Kinase inhibitors or other Bruton's Tyrosine Kinase inhibitors
• Have a positive result for hepatitis B surface antigen/antibody, hepatitis B core antibody, hepatitis C virus antibody or human immunodeficiency virus antigen/antibody at screening
• Have been treated with Oral steroids at dose above 10 mg/day of prednisone or prednisone equivalents
• Have a diagnosis of Felty's syndrome
• Have a positive result of the QuantiFERON®-tuberculosis (TB) Gold test or a T-spot ®-TB test at screening
• Have a positive result of β-D-glucan at screening