You can install git package in your Intel-Edison board easily, If you have install yocto operating system just following the steps to be installed git.
Login into your intel Edison, find out your operating system version,
Poky (Yocto Project Reference Distro) 1.7.2 \n \l
Run the command,
Note: If you get the error Unknown package 'git'
If you may getting an error add repos to the feeds in base-feeds.conf,
Open text editor and add repos three lines,
src all http://iotdk.intel.com/repos/1.1/iotdk/all
src x86 http://iotdk.intel.com/repos/1.1/iotdk/x86
src i586 http://iotdk.intel.com/repos/1.1/iotdk/i586
Save and quit,
Note : Again, if you were getting same error you need to check your network connection.