You can use an option on the library homepage entitled Journal Search to enter the title of the journal or magazine you are looking for.
Be sure to take note of the limited years of coverage (if any) for each option.
Excellent starting point. Multidisciplinary article database offers access to more than 16,000 journals, magazines, and newspapers, including over 15,000 peer-reviewed journals.
A combination of Harvard's Anthropological Literature and Anthropological Index from the UK's Royal Anthropological Institute. It covers hundreds of anthropology and archaeology journals and other relevant scholarly sources, including essays and chapters from edited books, with significant full-text provision.
Comprehensive coverage of sociology and its sub-disciplines, with very good coverage of related areas of study, especially politics. In addition to full-text journals, it contains informative abstracts for core coverage journals dating as far back as 1895.
Full-text coverage of nearly 300 journals, including 262 peer-reviewed publications, "covering topics such as world religions, major denominations, biblical studies, religious history, epistemology, political philosophy, philosophy of language, moral philosophy and the history of philosophy."
Full-text content of more than 250 of the world's most respected scholarly law journals, covering "issues, studies, thoughts and trends of the legal world" -- constitutional law, criminal justice, environmental law, commercial law, ethical issues, etc. Chronological coverage varies among sources, with some extending back to the early 1990's.
A digital archive of over 1,100 important scholarly journals. All issues of each journal are included in full-text except for the most recent 2-to-5 years, based on JSTOR's agreement with the journal's publisher.