I think there are a lot of false assumptions in your question.
Rapport has nothing to do with frequency of communication, but with content and quality, which in turn has nothing to do with whether it's face-to-face or via mail/chat/carrier pidgeon.
I have a couple of good friends who I've rarely ever met in person and sometimes we don't even chat for weeks on end.
What it takes, specifically, to build rapport with somebody is very individual to that person and your interaction with them. With some you might 'just click', with others it might never become that close - which is not a bad thing at all, mind you.
Not everyone will like you, you're not the jerk whisperer.
Now there are high-level steps you can take to build up rapport.
- Pay attention to them. Ask questions and listen to/read their answers closely. Find out what they are like, what they like, what problems you might help them with. But don't interrogate them. It's best to find common ground first by watching them.
- Support them. In small but noticeable ways. Maybe they need help with some tool you know, or somebody to review a report they do. Stuff like that.
- Show them more of you. That's probably the hardest for people struggling in this area. Being open and vulnerable, though, is giving them the opportunity to build their end of this bridge. Build rapport with you. This may be struggles at work, interests outside work, geeking out about coffe, whatever defines you.
If you want to learn more on building rapport, there are courses and sources out there, that are far more detailed than a post here could hope to be, but this is, from my experience with the topic, what people just struggling to connect can do.