In the Code of Jewish Law1 it is written that a Torah scroll should be held in one's right arm (and rested on the right shoulder). This applies even if the one holding the Torah is left-handed. There are two verses that allude to this idea:
1) "From His right hand was a fiery Law for them" -- Deuteronomy 33:2. The Torah was given from G‑d's right hand, as it were, and we therefore hold it in our right hand, too.
2) "And His right hand will embrace me" -- Song of Songs 2:6. G‑d embraces us with His right hand, and we, in turn, embrace His holy Torah with our right hand.