SSIS - executing package from SQL Server by stored procedure
If you are using SSISDB (which I think you are?), you can Execute a set of standard stored procedures that are in the SSISDB. These are outlined in the MSDN Article here.

This article also states the permissions that are required to run these procedures. It sounds like you need to set up a SQL Server login which has these permissions. How to describe this is located here. You will need to do this with your existing Windows Authenticated user if it has permission to allocate permissions (ALTER ANY LOGIN or ALTER LOGIN permissions).

You may also need to create a user who is mapped to this login as described here.

Your question is not very specific so without further information about a particular problem you are having, it is difficult to give a clear answer.