こんにちは!くまかけです。
rbenv+ruby-build環境を利用してRuby2.2.1をインストールしました。
rbenv+ruby-build環境の構築はこちらを参考ください。

■Rubyのバージョンを確認します。

# rbenv install -l
:
2.1.0
2.1.1
2.1.2
2.1.3
2.1.4
2.1.5
2.2.0-dev
2.2.0-preview1
2.2.0-preview2
2.2.0-rc1
2.2.0
2.2.1
2.3.0-dev
:

■Rubyをインストールします。

# rbenv install 2.2.1

Downloading ruby-2.2.1.tar.gz...
-> http://dqw8nmjcqpjn7.cloudfront.net/5a4de38068eca8919cb087d338c0c2e3d72c9382c804fb27ab746e6c7819ab28
Installing ruby-2.2.1...

BUILD FAILED (CentOS release 6.4 (Final) using ruby-build 20150303)

Inspect or clean up the working tree at /tmp/ruby-build.20150316172323.20827
Results logged to /tmp/ruby-build.20150316172323.20827.log

Last 10 log lines:
./libffi-3.2.1/.libs/libffi.a: could not read symbols: Bad value
collect2: ld returned 1 exit status
make[2]: *** [../../.ext/x86_64-linux/fiddle.so] Error 1
make[2]: Leaving directory `/tmp/ruby-build.20150316172323.20827/ruby-2.2.1/ext/fiddle'
make[1]: *** [ext/fiddle/all] Error 2
make[1]: *** Waiting for unfinished jobs....
installing default libraries
make[2]: Leaving directory `/tmp/ruby-build.20150316172323.20827/ruby-2.2.1/ext/json'
make[1]: Leaving directory `/tmp/ruby-build.20150316172323.20827/ruby-2.2.1'
make: *** [build-ext] Error 2

libffi.aが無いって感じですね。。。

# yum install libffi-devel

==========================================================================================================================================================
 Package                                 Arch                              Version                                  Repository                       Size
==========================================================================================================================================================
Installing:
 libffi-devel                            x86_64                            3.0.5-3.2.el6                            base                             18 k

Transaction Summary
==========================================================================================================================================================
Install       1 Package(s)

# rbenv install 2.2.1
# rbenv global 2.2.1
# ruby -v
ruby 2.2.1p85 (2015-02-26 revision 49769) [x86_64-linux]

■参考資料

Rubyをrbenv+ruby-buildを利用してインストールする手順 (CentOS/RedHat)