Proto-Indo-European Roots

Root/Stem: *reg'-
Meanings:  to rule, to lead straight, to put right
Cognates: Greek réks (a king) - a Middle Greek word borrowed from Latin in the Medieval epoch
Latin regere (to rule), rex (a king, a leader), rectus (right, correct), Oscan regaturei' (, a leader, a guider)
Common Celtic *réks, gen. *régos (a king) > Old Irish (a king), Scottish Gaelic righ; indirect Irish -righ (right) 
Gaulish -rix (a king), pl. -riges - known from personal names including Vircingetorix
Welsh rhi (a king) - here r is lenited, Breton reizh (right, correct), Cornish ruy (a king), Middle Breton roe
Common Germanic *reik-, *rik- (to rule) > Gothic reiks (a leader), Old English ríce (a kingdom), also -ríc (a king), ríce (rich, powerful); Old High German riche (kingdom), Old Norse & Old Swedish ríki (kingdom), Old Frankish ri'ke
          indirect: Old English riht (correct), Gothic raihts, Old High German recht, Old Swedish reht, Old Frankish riuht, Old Norse rettr
Modern: Swedish ratt, Danish ret, Icelandic rettr, German recht, Faroese raettur, Afrikaans reg, Dutch richten (to straighten out)
Avestan raé (wealth, wealthy), raya (rich person) - a supposed word; rástar (a leader) 
Persian rahst (right, correct)
Sanskrit ráj-, rat.  (a king, a leader) 
Thracian rhesus, resos, rézos (a personal name meaning "king")
Slavic: some linguists suggested an Old Russian deity Sva-rog, which is quite unnatural, for Indo-European -g'- must have caused Slavic -z-; more reliable is Old Russian rez (profit) derived from the meaning "wealthy" of the same stem.
Notes: The first meaning of the word that is so spread in modern tongues, was "to lead right", "a leader" (Latin: Qualis rex, talix grex). That's why the meaning "right, correct" is much more ancient than the other one "wealthy, rich" which was born from the wealth of kings and leaders. 
The words like English "direct" are also derivatives, coming from Latin dis-rego to Spanish derecho, Potuguese direito, Rumanian drept, Ladin dret, Catalan dret, French directe