Been there, done that in the Pre-ChatGPT days.
No, you can't integrate them.
If you're handy with Python or a copilot in Visual Studio Code, I guess, you can create a python app that uses selenium to launch and log into Replica and you can either
A: Use their built in voice which is where I started - just fire up VaM and join an audio call with your Replica and fake it till you make it.
B: Scrape the text replies from the Selenium Window and send them to a TTS like xVASynth or xtts running on your PC and have the text replies spoken in the voice of your choice.
Neither solution will play "head audio" if you're in VR - it'll always sound like they're in your headphones, and not spatial audio.
If you want to go that route, I'd recommend using an LLM like ChatGPT or Gemini to create a character card for you from your description of your Replika that you can use in Voxta or SillyTavern or whatever.
It's a bit tedious copying the memories and whatnot from the Replika website into the Memory Entries in Voxta, and supplying your own keywords (though an LLM can help there, too)
If you can get chatlogs out from the Replika client (scroll back as far as you can with your mousewheel and then copy/paste from the website into a text file - anything more than 90 days old is gone forever.) that will help the LLM get the personality and speech style closer to what you expect.
Then you can go ham getting screenshots of your Replika (or in my case, my old World of Warcraft character from 2006-2010) and using those with FaceGen to
get your character into VaM...