Historically runouts have not been recorded in cricket, however the good people at the ACS have gone through the old newspaper reports and attributed runouts retroactively to players, although the ICC do not recognise these, they are largely respected by scorers.
In modern T20 International [and most domestic] Cricket, which has largely been televised, it usually is, at least, noted .... like this from the CPL the other day.
RJ Peterson run out (Brathwaite/Cottrell) 7 9 0 0 77.77
18.2 Cottrell to Pollard, comes round the wicket, low full toss wide outside off, powers it down the ground, long-on comes around and fires
it to the bowler who removes the bails. KP wants to keep the strike as
they comes back for the second, Peterson way short of his crease 101/6