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Wikipedia states that it's 5/16" (~7.9mm) while two or three sites list it as 7.75mm.
I'm a little bit confused. Do chain rollers differ in diameter? Does diameter differ between singlespeed and derailleur chains? If so, I'd like to know the diameter of the derailleur chain's rollers.
I've measured three well-used chains with vernier calipers. Below are the method and measurements. I'm assuming you mean External diameter of the roller in the chain.
TL,DR 7.66mm +0.04mm -0.02mm measured.
KMC X10 10speed chain with 4223 km 7.64mm
Old Shimano CN-HG93 9 speed chain with 3800 km 7.70mm
8 speed folder with cheap Clark chain, around 2000 km 7.64mm
Method - my calipers were binding on the inner plates, so to get a good reading I had to make the chain slack and then pull up a roller
BAD 
GOOD 
I used an old spoke as a hook to take the tension off while taking that photo.
As the OP mentioned, Wikipedia asserts that the roller diameter is 5/16". The source appears to be American National Standards Institute (ANSI) standard #40 for chains. One webpage (note, not bicycle specific) appears to corroborate this. Chain #40 is listed as having a 1/2" pitch (corresponding to standard pitch for bike chains), a 5/16" roller diameter (about 7.9mm, as said), and a 5/16" roller width. We know that bicycles diverge from this roller width specification, because 11s chains are about 5.4mm wide, and 10s systems are around 5.9mm.
A 2019 Cyclingtips article made the statement below.
SRAM chains are one clear exception to using these suggested tools. Most chains on the market start with a roller that’s 7.63-7.65mm in outside diameter. SRAM’s chains are larger — for example, rollers from a Red 22 chain are 7.69-7.70mm, while an Eagle 12-speed chain uses rollers that measure 7.72mm. And SRAM’s new Flat-Top chain as part of the Road AXS groups is larger again (7.90mm).
For context, the first statement in the article was probably referring to the dimensions of 11s chains. Thus, we've shown that the chains in performance bicycles diverge from the official ANSI standard in roller diameter as well as width.
Chain checkers are common tools. This variance in roller diameter can throw off some types of chain gauges. Note that in the pic in the terminology index (latter link), the chain gauge pictured measures from the inside of one roller to the opposite side of one roller. The prongs are a set distance apart, and when the chain has worn to its wear limit (e.g. for 11s systems, replace chain at 0.5% for best results), the prong will drop between the two adjacent rollers. If the chain isn't sufficiently worn, the prong will contact the roller. Now, imagine what happens if the rollers are bigger than the gauge was designed for. The prong will not slip into the gap, i.e. the gauge will indicate that the chain is at its wear limit too late, which is bad for your cassette and chainring life.
The chain gauge pictured in the question I linked (first link) measures across the same side of the roller and is the correct design to use. However, at the time of writing, not all chain gauges can accommodate SRAM AXS road chains, which have a noticeably larger diameter than other common chains - although, ironically, their diameter is closer to the ANSI standard.
(NB: the above assertion is specific to SRAM AXS road chains, not Eagle MTB 12s chains. SRAM claimed that the larger roller diameter they used on AXS road improved chain wear, but I am not sure I see how and it raises the question of why they didn't do it to their Eagle chains also.)
