The answer is definitely "yes" but the question of "how many?" depends on how you define "resulting from."

In terms of very acute effects, there have been at least 4 acute fatalities due to nuclear testing. These include a Japanese fisherman exposed to fallout from the Castle Bravo test in 1954 (US health officials disputed that his death was caused by radioactivity, and instead thought it was because of his treatment regime, but either way it was his exposure that ultimately landed him there); a soldier and a child were killed as a result of the first Soviet H-bomb test in 1955 (details here — the blast wave reflected unpredictably off of an inversion layer in the atmosphere and was more powerful than it otherwise would have been); and there was an accident during an underground test at Nevada in 1984 that resulted in one fatality.

If you broaden that criteria, though, to people who got fatal cancers from being downwind of nuclear test sites, and died not immediately after the test but many years or decades later, the number grows to likely many thousands. Exact figures are hard to come by, but in both the USA and USSR and several other countries, there were significant populations of "downwinders" exposed to fallout during the years of atmospheric testing. In the case of the USA this included the Marshallese Islanders near its Pacific test site, as well as residents of Utah and Nevada near the Nevada Test Site.

If you broaden it out even more, to people worldwide whose chances of fatal cancers increased as a result of the increase in global radioactivity, the numbers get very vague but potentially extremely large, in the hundreds of thousands. This is a very hard thing to measure accurately. Atmospheric (above-ground) nuclear testing releases radioactive material that circulates globally. Generally speaking no single area is going to get what we would consider a dangerous amount of radioactivity. However large populations are going to get very small upticks in the probability of certain cancers. Those tiny increased risks add up to large numbers when you are talking about the entire population of the world (more or less), though no individual cancer is going to be able to definitively traced back to this cause.

Some estimates suggest that as many as 2 million people may have contracted fatal cancers as a result of Cold War nuclear weapons testing, but this may be too high of a guess. There are a lot of unknowns in these kinds of calculations. See: Arjun Makhijani and Stephen I. Schwartz, “Victims of the Bomb,” in Stephen I. Schwartz, ed., Atomic Audit, 395-431, on 395.

The demon core was a mass of plutonium that was eventually used in the Able nuclear weapon test.

While this core was still in the lab, it was directly responsible for the deaths of two scientists. In both cases, the core briefly and accidentally went critical, fatally irradiating one physicist per incident.

The second incident took place in a room full of people. Aside from the physicist who died (Louis Slotin), the criticality incident is possibly responsible for the death of two of the observers. These two individuals later died of cancer, although years later.

edit: Here is a primary source.

Would you include the fatalities linked to the development of the bomb as well? I thought there were several.