Can I get a dial-up modem working over SIP?

It might connect, but ordinary VoIP calls can be rough on modem signals. The connection depends on audio arriving with very little delay or distortion, and real-world networks can add jitter, packet loss, or call processing that makes it unreliable. If you try SIP, use an uncompressed codec such as G.711 where both ends support it, and turn off features like echo cancellation or noise suppression that can alter the modem tones.

For a controlled experiment, keep both endpoints on the same local network and use compatible analog telephone adapters. That avoids some internet routing problems, though it still may take trial and error.

If the goal is BBS access, I’d skip trying to carry modem audio through a SIP service. A USB modem connected to a small computer running a modem emulator such as tcpser can present a dial-up style interface while connecting onward to BBS systems over the network. It gives you the familiar modem experience without relying on a VoIP call to preserve every tone.

There are two different projects here: using a dial-up modem to reach the modern internet, and making a dial-up connection to a BBS. The second is much more practical. Even if you establish a modem link, many current websites are too demanding for the speed and old software involved, so a successful connection does not mean today’s web will be usable.

For a genuine modem-to-modem setup, you need a modem answering the call at the other end. A small computer can be configured as a dial-up access server, with an analog modem attached, so your computer dials it and gets a network connection. That is a different arrangement from simply dialing a BBS over a VoIP line, and it takes more setup, but it keeps the modem link between actual modems.