You can, but they're not practical weapons, either, really. Once decent ironworking was available, bronze became largely impractical for edged weapon manufacture, to the extent that you'd be unlikely to find one.
High quality pattern welded[1] steel swords were available in Roman times from at least 150 BC[2], and by 600 AD were ubiquitous. They were later mostly replaced by easier steel production techniques.
[1] https://en.wikipedia.org/wiki/Pattern_welding#Pattern_weldin...
[2] See the table of finds in https://www.tf.uni-kiel.de/matwis/amat/iss/kap_b/backbone/rb...