The Latin ablative re has become a word in English, meaning "regarding" or "with reference to" or something along those lines. This is also used in emails as an automatically generated prefix "Re: " to replies. Was the word re used in a similar fashion in antiquity, to indicate the topic at the start of a letter or a passage? In other words, did Romans use re in the same meaning as we do today in English?
Yes, it does have an ancient origin. See RFC 5332 (3.6.5):
When used in a reply, the field body MAY start with the string "Re: " (an abbreviation of the Latin "in re", meaning "in the matter of") followed by the contents of the "Subject:" field body of the original message. If this is done, only one instance of the literal string "Re: " ought to be used since use of other strings or more than one instance can lead to undesirable consequences.
Re was certainly used with the same meaning, as stendarr points out in another answer, but it was not used in the same manner. For example, Cicero did not start his letters with it, although there are examples of him using the word with the meaning "in the matter of."
There are many references in ancient texts showing the use of the word res in the ablative with the meaning "in the matter of." The Romans used res much like we use the word "thing" and they used it frequently. Even our word "republic" is from res publica which literally means "the public thing."
In a crazy sci-fi world where the Romans had email, I think using re just as we do would be completely consistent and appropriate.
Edit: From Cicero's letters:
I found abundant other examples among Cicero's letters of his use of re which I think could hold a meaning like what we're discussing, but this was the only one for which I was able to match the Latin text to an existing translation.
These examples are all in the body of his letters as he directs the reader's attention to some matter they've previously discussed. Re does not ever occur as a sort of subject line like we use it. There's also the example I mentioned in the comments.