To find a journal at Walker Library, click on "Journals A-Z" on the library's home page and type the title of the journal in the search box. A search for "American Journal of Sociology" retrieved these results. The results indicate which databases have the full text of the journal and the years of coverage.
From these results, you can see that the best place to find an article in this journal would be the database, "University of Chicago Press Journals," which has all the issues of this journal from 1895 to the present. If you want to use the journal in print or on microfilm, click the last result (Walker Library Building) to see what issues of the journal are available in the library.