Is encrypted database possible? I'm not a DBA but I've been asked to see if we can encrypt the data in sql server such that the admin, despite having access to SQL Server won't be able to see the data but application would still be able to query on it and read the data.

My limited knowledge of encryption tells me that if application encrypts the data then db won't be able to query it. If db encrypts the data then DBA can definitely read it.

So is there a way to prevent DBA from peeking into data but still be able to manage database?
You will need to encrypt the data within the application and store the encrypted values within the database.  Things like TDE and storage level encryption will not meet your requirements.