Apple - Computer modern font for OSX
OS X has never included Computer Modern as standard, only as part of the X11 system. The font was originally created by Donald Knuth using metafont so that he had a good font for his typesetting system, Tex, that he wrote to typeset his books on programming.
The modern versions were created to provide a good quality font for the X11/Tex project.
The Computer Modern home page is here: http://canopus.iacp.dvo.ru/~panov/cm-unicode/ Note that these are the version with the "Blue Sky" font hinting that almost everyone uses these days rather than the Knuth originals.
You will want the "otf" (Open Type Font) file which at the time of writing is ftp://canopus.iacp.dvo.ru/pub/Font/cm_unicode/cm-unicode-0.6.3a-otf.tar.gz
If you open the application Font Book
you can have a look at the fonts installed on the System and install new ones using drag and drop.
On a final note, if you arrive at this answer and are going to be doing serious typesetting with Computer Modern you may wish to install the entire American Mathematical Society AMSFonts package available here - it's even packed as a TEXMF directory structure if that is of use to you. Otherwise it contains Postscript fonts well down in the folder hierarchy that can be easily installed on a Mac. It includes other useful fonts and extensions to the basic Computer Modern set. All are free under the SIL Font License.
For the users that are more comfortable with using Terminal. You can also install it through Brew.
brew tap homebrew/cask-fonts
brew cask install font-computer-modern