The most secure that you could ever make any application is not to store a password at all. You would ask the user to supply their username and password in order to form a connection to the database.
In your case though, you need to connect as a specific user with a password saved. The location of this password is outside of Oracle's control and you will therefore have to encrypt the password yourself. From Oracle's perspective, your application is some user attempting to connect. The encrypted password would be saved either in your code file (hopefully not) or in a config file. Your application code would have to read the encrypted password, decrypt it, and then supply it as input into your connect function. After that, Oracle takes care of the encryption between the application and the database itself along the SQL*Net connection.
There are hundreds of encryption algorithms and components that could be used. You need to decide on how important the data is and how high the fences need to be (so to speak). If you just want to hide the password from prying eyes, then a simple base64 encode will probably suffice.
Always remember though, that your code file containing your decrypt and connect code could be viewed and then used to decrypt and show your password.