There probably is but it's in Japanese.
Why no Shogi.com?

Years ago I stumbled upon a Shogi telnet site by mistake while looking for alternate chess sites. I talked to some of the people. One offered to teach me the game. I don't know if a gui was available.

But you miss all the fun playing shogi online. There is an art to flicking the pieces on the board.
I'd love to play Shogi in person! Sadly, opponents are hard to find outside of Japan.

real talk, i feel like it wouldn't be such a big task if chess.com just took its existing infrastructure, which works great for chess, and just made a Shogi mode. i was thinking about this earlier today - they could probably even do other chess-like games, namely Go.
if they literally can just do it - as in, if it's not a technical challenge for devs, and the only barrier is time or money - they'd probably dominate the shogi and go online spaces very quickly. chess, shogi, and go are all very similar games: white and black take turns, you move pieces, you capture pieces... the only difference between go and chess anyway is the win condition, but they even have that covered, eg any of the chess variants where you win by doing something other than getting mate (antichess??)
Maybe have the same features and modes like in Chess.com, and you get Shogi.com.