Background Psychiatric comorbidity with a chronic disease is linked with poor patient outcomes. Therefore, the current research assessed the correlation of rheumatoid arthritis (RA) with depression and anxiety disorders. Methodology A prospective observational study was undertaken at a public sector hospital between December 2020 to June 2021. All individuals who presented with rheumatoid arthritis were included in the study. A healthy cohort acted as the control group. Depression and anxiety were assessed using the Hamilton depression rating scale (HDRS) and the Hamilton anxiety rating scale (HAM-A), respectively. The patients were inquired about their gender, age, and duration of RA. Further stratification was done using the Chi-squared test. A p-value of <0.05 was decided as the cut-off for significance. All data from the patients were collected in a predefined pro forma. Results A total of 169 patients with RA and 85 healthy controls were enrolled in the study. The mean depression score among patients with RA was 19.65 ± 1.44 versus 14.4 ± 1.31 in the control group (p<0.001). Moreover, the mean anxiety score in patients with RA was 19.44 ± 2.4. About 71% of patients with RA were diagnosed with psychiatric issues, while only 7.1% of individuals in the control group had either depression or anxiety (p<0.0001). Furthermore, it was found that the majority of the patients with RA had depression with a frequency of 70 (58.3%), while only six participants in the control group had depression. None of the participants had moderate or severe depression. However, 16 (69.6%) patients with RA had major anxiety issues. In 27 patients, mixed anxiety-depression disease was diagnosed. Out of these, 23 (85.2%) had the depression-dominant mixed disorder. Conclusion The present study highlighted the alarming incidence of depression and anxiety among patients with RA. Furthermore, it also indicated the relationship between severity of psychiatric comorbidity with chronic rheumatoid arthritis in our population. Further large-scale studies are needed to ascertain the demographic confounders that may help predict psychiatric disorders among patients with RA.