Can international campus students who enter in January complete an internship in the United States during the following summer term?

No, not usually. The US Department of Homeland Security requires that international students be enrolled full-time in and complete two semesters of coursework in F-1 status before applying for off-campus work authorization, commonly called Curricular Practical Training (CPT). Students who start the MEM program in the fall in F-1 status meet this requirement. However, students who begin the program in January in F-1 status are required to be enrolled full-time for the spring semester and the following fall semester before becoming eligible to apply for off-campus work authorization. They may then apply for CPT for the following spring semester, or they may choose to continue as a full-time student in the following spring semester and apply for CPT for the following summer.