GPG encrypt a file with only a passphrase (no key storage needed)
What you want is called symmetric encryption -- where the same key is used for both encryption and decryption -- and yes, GnuPG can do it.
Use --symmetric or -c instead of -er RECIPIENT.
PS: You can combine the two modes so that a file can be decrypted by either the symmetric passphrase or by any of the RECIPIENT private keys.