When it comes to questions asking "Are there any Christians that do such-and-such" it's very hard to answer, because Christianity is a very diverse group and there are highly likely to be at least a few Christians that do almost anything. However in this case I'm going to go out on a limb and answer "No". Here are my reasons.
- The first part of Leviticus deals with animal sacrifice. Not just occasional sacrifice, but regular and frequent. It's unlikely that Christians would be doing this without us having heard about it. Even Jews have not followed the sacrifice rules in Leviticus since around 70AD. Additionally it is explicitly taught in Christian scripture that Christ's sacrifice has made animal sacrifices unnecessary. It's a key part of Christianity not to make the Levitical sacrifices.
- A later part of Leviticus deals with clean and unclean food. Again Christians were explicitly told by God (as recorded in Acts 10) not to follow those rules.
There are Christians who spend most of their time interacting with the Jewish community, and some of them follow the dietary rules of Judaism, to avoid giving offence. That's approved of in scripture. However even they will not follow the animal sacrifice rules.
Summary: I'm pretty confident in being able to answer "no".