(1) Background: Rational use of medicines (RUM) and their assessment is important to ensure optimal use of resources and patient care in hospitals. These assessments are essential to identifying practice gaps for quality improvement. (2) Methods: Assessment of adherence to WHO/ International Network for Rational Use of Drugs core prescribing indicators among out-patients in 2021 was conducted at the University Hospital of the Kwame Nkrumah University of Science and Technology in the Ashanti region of Ghana. We reviewed electronic medical records (EMR) of 110,280 patient encounters in the year which resulted in 336,087 medicines prescribed. (3) Results: The average number of medicines prescribed per encounter was 3 with generics being prescribed in 76% of prescriptions. Injections were prescribed in 7% of encounters while 90% of medicines were from Ghana’s Essential Medicines List 2017. (4) Conclusions: With the exception of patient encounters with injections, all prescribing indicators assessed in this study did not meet WHO optimum levels providing targets for quality improvement in RUM. Implementing prescribing guides and policies, regular audits and feedback as well as continuous professional development training may help to improve prescribing practices in the hospital.