Cognitive deficits are commonly seen in people with arthritis. However, previous studies focused primarily on small-sized clinical samples. There is a need for cohort-based studies, which are characterized by high generalizability. In addition, these studies mainly focused on attention, memory, and executive function. However, cognition is not a single concept, but includes other cognitive domains, such as verbal fluency and arithmetic abilities. Thus, we aim to explore how arthritis can affect cognitive abilities, including episodic memory, semantic verbal fluency, fluid reasoning, and numerical ability by using a large cohort from the United Kingdom. The main findings were that people with arthritis have significantly lower immediate word recall (t(2257) = −6.40, p < 0.001, Cohen’s d = −0.12, 95% C.I. = [−0.16, −0.08]), delayed word recall (t(2257) = −5.60, p < 0.001, Cohen’s d = −0.11, 95% C.I. = [−0.14, −0.07]), semantic verbal fluency (t(2257) = −3.03, p < 0.01, Cohen’s d = −0.06, 95% C.I. = [−0.10, −0.02]), fluid reasoning (t(2257) = −3.96, p < 0.001, Cohen’s d = −0.07, 95% C.I. = [−0.11, −0.04]), and numerical ability (t(2257) = −3.85, p < 0.001, Cohen’s d = −0.07, 95% C.I. = [−0.10, −0.03]) compared to what they would expect given their demographics. Interventions are needed to improve cognitive abilities in people with arthritis.