I estimate that no more than 300,000 people dance tango worldwide.
Let me share my method of estimation for the total number of tango dancers (from which my criteria of being a "tango dancer" - used only for the purpose of this calculation - also becomes clear). I started with trying to figure out the approximate number of milongas worldwide. Fortunately there is a long-established website dedicated to collecting all milongas worldwide called milongas-in.com. At the time of this writing there are 2,419 milongas listed on this site, the majority as a regular weekly milonga. Unfortunately the quality of listings is not even and/or not very up-to-date, so for large cities known for their vivid tango life I did some manual search and correction using local milonga calendars. For example for larger cities in Argentina and Uruguay milongas-in.com seems to be off with a factor of ~4, with the exception of Buenos Aires where it is off with a factor of 8. In larger tango centers in Europe (Berlin, Istanbul etc) milongas-in.com seems to be off with a factor of ~1.5-2, while in smaller tango cities / countries it even seems to overestimate the number of weekly milongas. I suspect the difference in listing quality is related to the intensity of tango life in given destinations (in places with less intense tango life organizers may pay more attention to be listed and/or there is a higher turnover rate for milongas resulting in more defunct milongas staying listed on the site). So I decided to adjust the milongas-in.com numbers with a factor of 8 for Spanish speaking countries and with a factor of 2 for all other locations, plus added an upper estimation for the number of tango festivals / marathons / encuentros / camps per week (equating each of them with 5 milongas, or, as we will later on see, 250 people). As a result we get that there are ~6000 milongas per week worldwide.
If we further guesstimate that an average milonga is attended by ~50 people (which I believe to be an upper estimate for the average attendance) and assume that on average a dancer attends a milonga once a week (another estimation resulting in an exaggerated figure, for the harder core tangueros/tangueras who make up the significant portion of the milonga population dance more frequently, while those who dance less than, say, once a month, may not quite qualify as a "tango dancer") we arrive at the final upper estimation of 300,000 people dancing tango worldwide.
Given the upper estimations the true number of active tango dancers is probably less than 300,000, maybe significantly so. On the other hand there is clearly more interest in Argentine tango dance music than what is apparent from milonga attendance. For instance Argentine Tango Radio has ~500,000 listeners from ~70,000 unique IP addresses a month; if these 70,000 listeners were all drawn from the pool of active tango dancers that would mean that roughly every 4th active tango dancer is also a listener of the radio. While this would be quite nice, I believe it is rather the case that there is a large number of people who like to listen to tango dance music but is not (yet?) attending milongas.
Another number indicating a much larger interest in tango comes from Youtube statistics. For instance the video for the Argentine tango flash mob I organized also picks up ~300,000 viewers each month. I doubt that all active tango dancers watch this video once a month; rather, there is a large untapped potential of people who are interested in Argentine tango but don't get to the point of attending milongas.
So, let's reach out!