Not as I understand it. The intent of the Scottish Parliament is to be very open to public petitions, so there are no citizenship or residence requirements - to some extent, that is understandable. As there is no such thing as Scottish citizenship (only British citizenship) it would be very difficult to restrict such a right only to Scots and they also did not want to exclude non-citizens resident in Scotland (and therefore subject to Scottish law) or those who are part of the Scottish diaspora overseas. But it does allow for a degree of foreign interference in Scots issues.
The plus side is that a petition in which a person has no clear standing can be dealt with very quickly - the requirement for it to be considered is not onerous - it can be dismissed quite quickly unless it clearly relates to an important issue in Scots law.