Background and objective Procrastination, which refers to the act of unnecessarily delaying the beginning or completion of an assigned task, is a widespread but often neglected problem among college students. Postponing a task can impair academic performance or lead to stress and poor mental well-being. A knowledge gap exists in understanding the cyclical nature of the relationship between anxiety and procrastination, wherein anxiety leads to procrastination, which in turn exacerbates anxiety. In light of this, we aimed to assess the level of procrastination and anxiety among college students and to correlate the relationship between their procrastination and anxiety status. Methodology A cross-sectional analytical study was conducted among 347 graduate students from various disciplines at a tertiary care hospital in Puducherry, India. A convenient sampling technique was employed to recruit the participants, and data were collected using the validated Procrastination Assessment Scale for Students (PASS) and the Hamilton AnxietyRating Scale (HAM-A). Results Our findings showed that about 124 (35.7%) participants reported weekly reading assignments as the most frequently procrastinated task, with a mean score of 3.15 ± 1.02, followed by studying for exams and writing term papers. The most commonly reported reason for procrastination was evaluation anxiety, followed by low self-esteem and perfectionism. A significant number of students (157, 45.2%) had mild anxiety, and 58 (16.7%) students were found to have severe anxiety. A Spearman correlation coefficient of 0.26 (95% CI: 0.16 - 0.36) was observed between the overall procrastination score and HAM-A score, which indicated a weak positive correlation and was statistically significant (p<0.05). Similarly, a weak positive correlation was found between task aversiveness, fear of failure, and anxiety levels. Conclusions Procrastination is positively related to anxiety but the relationship is weak. Understanding and addressing the underlying anxiety or stress can be a key to managing procrastination among college students.