AMA Style uses standard abbreviations for journal titles when making references. A list of many journal abbreviations can be found in the AMA Manual of Style (473-479). Additional abbreviations can be searched in the PubMed Journal Database.
For any unlisted journals, the AMA Manual instructs us to abbreviate them "according to the US National Library of Medicine's current Fact Sheet" (472). The referenced Fact Sheet is: Construction of the National Library of Medicine Title Abbreviations.
Online Guides to Using AMA Style
AMA Reference Citation Format (New York Medical College)
AMA Style (Purdue OWL)
AMA Style Guide (University of Washington)