I've done all the research I can, but I can't come up with an answer. Perhaps a professional on the subject can better inform me?
Politics.StackExchange usually leans towards the more liberal side, and I am mostly liberal myself, and this is definitely a popular and contentious topic at the moment, but answers like "They don't even exist", "Actually, it is not an organization, it's a movement so nobody "belongs"" and (unrelated to this question) "They are literally called "anti-fascism" how can they be the bad guys when they're against fascism?" is the standard boiler-plate response given by anybody who considers themselves antifa and is trumpeted as far and loud as possible by their "allies" in the media and government. There are plenty of well known cases of reporters, mayors, governors, council members who have outright stated that they support antifa, following some violence or "direct action" and then they usually convey some variation on the above quotes.
Groups and organizations that attempt to operate clandestinely or through loosely related "cells" are, of course, more difficult to count but to say they are uncountable or too amorphous is absurd. There will always be some fluctuating amount of people who consider themselves to be actual members of [group] who do the majority of the organizing/ heavy lifting/ promoting. Then there is a usually larger number of people that consider themselves allies, or may be aligned with some goal and will lend support in the case of [event]. Then there is the population of people that agree with their goals/ methods/ whatever but won't get directly involved. All of these can be estimated and so there is no reason to state it is not possible except to dissemble or misdirect.
Can I estimate these populations myself? Unfortunately, no. I wouldn't even know where to begin, but anybody can do a search online and see countless twitter accounts for different cities and neighborhoods (however much weight you want to put in to that), local crew web pages detailing actions and events going back for years, accounts of members going to Syria to get combat training. It is not a small group and they are definitely not shy about making their (usually anonymous) online presence known.
As far as I can tell their increasing violence (probably commensurate with an increase in membership since Trump became president) against anybody considered conservative over the past 6 or so years has even spawned some of the violent far-right groups as opposition, or at least caused them to coalese into an actual organization (one that also has a population that can be counted) that have been showcased by the media lately. Search for "anti-antifa" protests for more on that subject.
I wish I had a more concrete answer for you.
Unrelated to this specific question, but very on topic, this seems to be the first time that antifa has tried to seriously and systematically control/ shift the direction/ accelerate the intensity or violence of BLM demonstrations.
About the Trump inaguration, CNN stated: "Many of [more than 200 people] arrested identified themselves as part of the Antifa movement."
Here are some other related articles:
(I thought this article had a ton of references, but they're just links to they're own site)
A paper on Antifa that tackles the same definitional problem, though I think it is only focused on Europe
Antifa doesn't have membership
Antifa is a political movement not an organization. It's a bit like asking "How many members does the Black Lives Matter (BLM) movement have?" It represents a fundamental misunderstanding of what antifa is.
Antifa doesn't have a central organization or membership. It's a political movement dating back to the 1920 of regular people who choose to act out against fascism (hence the name anti-fascist, shorted to antifa), in whatever way they see fit to do so.
Some antifa activists do form small decentralized groups of like-minded individuals, but it's impossible to know how many such groups there are or how many "members" they have in total, and that wouldn't include all the individuals who are also anti-fascist.
There have been some comments (now moved to chat) that the FBI might have estimates. If they do, I haven't been able to find them, so they're probably not public. What can be easily found is info (backing up CrackpotCrocodile's answer) like this piece of 2019 news
At a Senate Judiciary Committee hearing on Tuesday, [Senator Ted] Cruz mentioned a recent Portland protest where journalist Andy Ngo was beaten up by black-clad activists, and an attempted attack on a U.S. Immigration and Customs Enforcement center in Washington state. "I am concerned that these are not isolated instances but rather this is a pattern, an organization that is engaged in masked, anonymous, violent terrorism," Cruz said.
FBI Director Christopher Wray told Cruz the agency is "absolutely concerned about violence committed on behalf of any ideology." But "the key there," said Wray, is that "the FBI doesn't investigate ideology, we investigate violent criminal activity."
Wray continued, essentially telling Cruz that you can't just criminally investigate anyone associated with an ideological movement because a few proponents of that ideology have done bad things. The FBI definitely "considers Antifa more of an ideology than an organization," Wray said.
Side note: Trump is not fond of Wray, so the answer to that issue--how the FBI sees Antifa--might change with new (FBI) leadership, who knows....