Actually, i believe the charter established the house of commons.
No, but it was part of the process of the development of Parliament in England. Magna Carta required that the King had to have the consent of a council in order to levy taxes, which meant for the first time that a King had no choice under certain circumstances to convene such a council (previous Kings had done so, but were not legally required to). This idea that the King had to call and consult a council is what developed into Parliament (and the term started being used in the 1230s). From 1258, Henry III was compelled to summon Parliament at least three times a year and that began the idea of Parliament as something approaching a standing body with regular sittings.
The first Parliament to involve commoners was convened in 1265, fifty years after Magna Carta. After that, it became normal for common representatives to be summoned to Parliaments, but until 1341, both the Lords and Commons sat as a single chamber - they were only divided then into separate Houses.