Bishop Tartaglia's comments came after the most senior Scottish catholic, Cardinal Keith O'Brien, said legalising same-sex marriage would "shame Scotland in the eyes of the world".
Ms Davidson, who is gay, has been among those giving cross-party support to a same-sex marriage bill which is being brought forward by the Scottish government, while Cardinal O'Brien has been a strong critic of the plans.
Vice-President Joe Biden, New York Governor Andrew Cuomo, and Maryland Governor Martin O'Malley - seen as possible presidential hopefuls - have also backed same-sex marriage.