After a long gestation period, JAGS 4.0.0 was finally released last week. If you go to the project page on Sourceforge then you should see an appropriate download link for your platform (binary packages for Windows and Mac OS X; source tarball for other platforms). Binary packages are also available for some Linux distributions. See the JAGS homepage for details.
Mac users should note that you need OS X 10.9 or later (i.e. Mavericks, Yosemite, or El Capitan). Older releases are no longer supported.
The rjags package for R has been updated to work with the new release of JAGS. It is not yet uploaded to CRAN, and the version of rjags that is available on CRAN (rjags_3-15) does not work with JAGS 4.0.0. However, you can download rjags_4-3 from Sourceforge. Again, binary packages are available for Windows (.zip) and Mac OS X (.tgz).