I found this nice and easy-to-follow guide on how to download the GIT source and compile it yourself (and install it). If the accepted answer does not give you the version you want, try the following instructions:

http://tecadmin.net/install-git-2-0-on-centos-rhel-fedora/

(And pasted/reformatted from above source in case it is removed later)

Step 1: Install Required Packages

Firstly we need to make sure that we have installed required packages on your system. Use following command to install required packages before compiling Git source.

# yum install curl-devel expat-devel gettext-devel openssl-devel zlib-devel
# yum install  gcc perl-ExtUtils-MakeMaker

Step 2: Uninstall old Git RPM

Now remove any prior installation of Git through RPM file or Yum package manager. If your older version is also compiled through source, then skip this step.

# yum remove git

Step 3: Download and Compile Git Source

Download git source code from kernel git or simply use following command to download Git 2.5.3.

# cd /usr/src
# wget https://www.kernel.org/pub/software/scm/git/git-2.5.3.tar.gz
# tar xzf git-2.5.3.tar.gz

After downloading and extracting Git source code, Use following command to compile source code.

# cd git-2.5.3
# make prefix=/usr/local/git all
# make prefix=/usr/local/git install
# echo "export PATH=$PATH:/usr/local/git/bin" >> /etc/bashrc
# source /etc/bashrc

Step 4. Check Git Version

One completion of above steps, you have successfully install Git in your system. Let use following command to check git version

# git --version

git version 2.5.3

I also wanted to add that the "Getting Started" guide at the GIT website also includes instructions on how to download and compile it yourself:

http://git-scm.com/book/en/v2/Getting-Started-Installing-Git