The php-mbstring is part of Redhat's server optional packages. If you have a current subscirption all you need to do is to enable this repository using:
[root@rhel7 ~]# subscription-manager repos --enable=rhel-7-server-optional-rpms
and use yum to install php-mbstring. In case that you do not have a current Redhat subscription you can install php-mbstring directly from IUS project repository:
[root@rhel7 ~]# wget http://dl.iuscommunity.org/pub/ius/stable/Redhat/7/x86_64/ius-release-1.0-13.ius.el7.noarch.rpm
[root@rhel7 ~]# wget http://dl.fedoraproject.org/pub/epel/7/x86_64/e/epel-release-7-2.noarch.rpm
[root@rhel7 ~]# rpm -Uvh *release*.rpm

Now simply execute yum command to install php-mbstring:
[root@rhel7 ~]# yum install php-mbstring
Installed:
    php56u-mbstring.x86_64 0:5.6.0-2.ius.el7                                                                                                                            

Dependency Installed:
  php56u-cli.x86_64 0:5.6.0-2.ius.el7      php56u-common.x86_64 0:5.6.0-2.ius.el7  
  php56u-pear.noarch 1:1.9.4-21.ius.el7  php56u-pecl-jsonc.x86_64 0:1.3.6-2.ius.el7 
  php56u-process.x86_64 0:5.6.0-2.ius.el7  php56u-xml.x86_64 0:5.6.0-2.ius.el7    

Complete!
Restart httpd:
[root@rhel7 html]# service httpd restart
Redirecting to /bin/systemctl restart  httpd.service
If you alredy had PHP installed on your server you may get a Transaction check error. In this case we need to replace entire PHP stack:
[root@rhel7 ~]# wget http://dl.iuscommunity.org/pub/ius/stable/Redhat/7/x86_64/yum-plugin-replace-0.2.7-1.ius.el7.noarch.rpm
Install yum replace package:
[root@rhel7 ~]# rpm -i yum-plugin-replace-0.2.7-1.ius.el7.noarch.rpm 
and replace entire PHP stack:
[root@rhel7 ~]# yum replace php --replace-with php56u
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