Measure compilation time of stored procedure
Yes, you can get this information. It is buried inside properties of the select statement in an actual execution plan. To do that:


Set Actual Execution plan to on
Execute your SP with recompile option
Go to Actual Execution plan, choose 'select' part
Go to properties (Press F4) and there you can see CompileTime


However, I'm not sure how accurate or what measures this information displays. 

I am assuming, you want to discover how much it does affect your performance. You can search this article for 'compile time' https://technet.microsoft.com/en-us/library/cc966540.aspx