As title suggested, I haven't been able to find a good way to install aws-cli (https://github.com/aws/aws-cli/) without having the root access (or equivalent of sudo privileges). 
The way Homebrew setup on Mac is hinting at it may be possible, provided that a few directories and permissions are set in a way to facility future installs. However, I have yet to find any approach in Linux (specially, Red Hat Enterprise Linux or CentOS distroes). 
I am also aware of SCL from RHEL (https://access.redhat.com/documentation/en-US/Red_Hat_Enterprise_Linux/6/html/Developer_Guide/scl-utils.html) But again, it requires sudo.