No.
A "raw transaction" is simply a transaction.
I guess you are referring to the getrawtransaction CLI command from core ?

You can use the -v (verbose) flag to get more information about that transaction.

However, a private key is never included in a transaction.
The private key is used to sign a transaction.

Transactions are being broadcasted into the network. They simply can not contain your private key without the whole system being worthless and broken.