First of all, "Always on" is an umbrella name for two technologies for HA (High Availability): Failover cluster instances (FCI) and Availability Groups (AG). Most people incorrectly use Always On to mean AG, so I will assume that this is what you have in mind.
To use AGs for HA, you first in need a Windows Failover Cluster, to set up that, you need to be a Windows administrator. I don't know on the top of my head, the exact permissions needed to create an availability group in SQL Server, but if you look at the topic for CREATE AVAILABILITY GROUP to find out. But in practice, setting up an AG is a task for sysadmin.