Antibiotics are a strong risk factor for Clostridioides difficile infection (CDI), and CDI incidence is often measured as an important outcome metric for antimicrobial stewardship interventions aiming to reduce antibiotic use. However, risk of CDI from antibiotics varies by agent and dependent on the intensity (i.e., spectrum and duration) of antibiotic therapy. Thus, the impact of stewardship interventions on CDI incidence is variable, and understanding this risk requires a more granular measure of intensity of therapy than traditionally used measures like days of therapy (DOT). We performed a retrospective cohort study to measure the independent association between intensity of antibiotic therapy, as measured by the antibiotic spectrum index (ASI), and hospital-associated CDI (HA-CDI) at a large academic medical center between January 2018 and March 2020. We constructed a marginal Poisson regression model to generate adjusted relative risks for a unit increase in ASI per antibiotic day. We included 35,457 inpatient encounters in our cohort. Sixty-eight percent of patients received at least one antibiotic. We identified 128 HA-CDI cases, which corresponds to an incidence rate of 4.1 cases per 10,000 patient-days. After adjusting for known confounders, each additional unit increase in ASI per antibiotic day is associated with 1.09 times the risk of HA-CDI (Relative Risk = 1.09, 95% Confidence Interval: 1.06 to 1.13). ASI was strongly associated with HA-CDI and could be a useful tool in evaluating the impact of antibiotic stewardship on HA-CDI rates, providing more granular information than the more commonly used days of therapy.