I'm preferably looking for a SQL query to accomplish this, but other options might be useful too.
SELECT LAST_DDL_TIME, TIMESTAMP
FROM USER_OBJECTS
WHERE OBJECT_TYPE = 'PROCEDURE'
AND OBJECT_NAME = 'MY_PROC';
LAST_DDL_TIME
is the last time it was compiled.
TIMESTAMP
is the last time it was changed.
Procedures may need to be recompiled even if they have not changed when a dependency changes.