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,

# cat /etc/issue
Poky (Yocto Project Reference Distro) 1.7.2 \n \l
# cat /etc/version 
weekly-159.devkit-2.0


Then,

Run the command,
 
​# opkg install git
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,
 
# vi /etc/opkg/base-feeds.conf


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,

wq!

Finally,
 
# opkg update

# opkg install git

Note : Again, if you were getting same error you need to check your network connection.