A few years ago, I was told by a member of the Society of Scottish Armigers that, for US citizens, you only need to show descent from someone who was a subject of The Crown (the King/Queen) prior to Sept 3, 1783 (the date the Treaty of Paris was signed ending the Revolutionary War). This person didn't necessarily have to be Scottish, just "a subject of the crown", but I think that's the general presumption. Lord Lyon would then grant arms in honor of this person. If your surname is from one of the clans (in my case Scott), the arms would be similar to the clan chief's, with some emblem/device to note it is a different branch of the family name. It is suggested that a large group of family members (sibling and cousins) share the cost of this grant, since they may all use this as the basis for their own grants.

Once the grant in honor of this person takes place, THEN arms may be matriculated from them with the appropriate differencing per the rules of heraldry. Lord Lyon (or an officer of his court) will work with you for any additional/unusual/personal elements you may wish to have. You can even change the motto if you so desire.