The following licenses are in use for R or associated software such as packages.
R as a package is licensed under GPL-2 | GPL-3. File doc/COPYING is the same as GPL-2.
Some files are licensed under 'GPL (version 2 or later)', which includes GPL-3. See the comments in the files to see if this applies.
Some header files are distributed under LGPL-2.1: see file COPYRIGHTS (on the SVN server).