Charles Edward Stuart was the Jacobite claimant to the throne of Scotland. Jacobites believed that King James II remained the King of Scotland even after the "Glorious Revolution" of 1688.

James II was overthrown by the glorious revolution because although he was born a protestant he later converted to Catholicism in 1668.

The eldest daughters of James II were raised as protestant on the orders of their uncle Charles II. After Charles II died in 1685 James II became the King of Scotland. Protestants were willing to abide having a Catholic King since his daughters were protestant, and after James II died England and Scotland would have a protestant monarch again.

However in 1688 James II had a son, James Francis Edward Stuart (also known as the old pretender), this caused a group of Protestant nobles to overthrow James II and place his daughter Mary II and her husband William III on the throne.

The Jacobites continued to claim the throne with little success until Anne I, the last Stuart monarch died in 1715. Afterwards the King of Great Britain would be George I who was distantly related to the royal family and who only became King due to the Act of Settlement of 1701, which among other things banned Catholics from inheriting the throne.

According to Jacobites the descendants of James II youngest sister Henrietta Anne are the legitimate claimants to the Scottish throne. After the death of the Cardinal Duke of York in 1807 who was the last descendant of James II, the Jacobite claim passed through the Houses of Savoy, Austria Este, and Wittelsbach. The current Jacobite claimant is Franz, Duke of Bavaria.

The claim of Franz would be completely legitimate according to the laws of Scotland prior to the "Glorious Revolution".

Franz does not actively claim the throne but there are at least enough people in Britain who believe he is the King that they have an active website and an annual dinner. They call Duke Franz of Bavaria "Francis II." Here is a link to their website http://www.royalstuartsociety.com/succession.html

Other possible claimants to the Scottish throne are the illegitimate children of Charles II. His eldest son James Scott, 1st Duke of Monmouth did claim the thrones of England and Scotland, Monmouth claimed his parents had been married which would make him the legitimate claimant. If this was true then his current heir Richard Scott, 10th Duke of Buccleuch would be heir to the throne of Scotland.

Something that strengthens his claim is the fact that Richard is a Scottish Duke, lives in Scotland, is the largest private land owner in Scotland, and is the Lord High Commissioner to the General Assembly of the Church of Scotland.

Another possible line of claimants are Clan Stewart, which are the clan that the house of Stuart is descended from. Clan Stewart's main cadet branch is the Stewarts of Gallaway, making Randolph Keith Reginald Stewart, Earl of Galloway, Lord of Garlies, Baronet of Corsewell and Burray the one with the strongest claim to lead clan Stewart

So to answer the question you've actually asked, the heir to the "Scottish throne", if we were to assume that it would still exist, is Prince Charles. When Elizabeth I of England died in 1603, the crown passed to her cousin (several times removed) James VI of Scotland. James and his descendants ruled both Kingdoms (with a brief interlude in the 1650s) until the Act of Union when Scotland and England were subsumed into the United Kingdom.

The two were still independent of each up until this time though, and being King of Scots did not automatically make one the King of England or vice versa. For example, when Charles I was executed in 1549, the English Monarchy was abolished. However, his eldest son was proclaimed King Charles II by the Scottish Parliament in 1549, and ruled until 1651 when he was defeated by Cromwell and fled to France for the next 9 years until both monarchies were restored in 1660.

When James VI/I's last descendent in the Male Line died (Anne, in 1714), the throne passed to his Great-Grandson George-Augustus of Hanover, from whom all future Monarchs of the United Kingdom are descended, and hence, Prince Charles would, if an independent Scotland were to be declared a monarchy, be the heir.

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But what I think you're actually asking is "Who is the Senior Jacobite claimant?", which isn't the same thing. The simple answer to that is Francis Duke of Bavaria, but it's actually more complicated than you may think.

So as a bit of context: When Charles II died in 1685, both thrones passed to his popular younger brother James, Duke of York. Now, the Stuart family have a very a strange relationship with religion, with very few little consistency between them as to their confession, and most were out of touch with their kingdoms. James VII was the climax of this though, as an actual Catholic he was completely isolated from the vast majority of his subjects. This, along with complications of syphilis and the fact he was generally out of touch with reality, meant he burned through his goodwill very quickly. The only good thing, from the perspective of his subjects was that both of his daughters were Protestant. However, in 1688 his wife gave birth to a male child who survived, and would be expected to be raised Catholic.

This ultimately lead to James' deposition in 1688. While this was primarily enacted by the English, by now the Scots weren't any more impressed at all, particularly as he was alienating both the factions of the Scottish Kirk, and his son-in-law William of Orange, had massive appeal to both Presbyterian and Episcopalian factions. As such, both Scotland and England held that James VII/II abdicated by fleeing to France and as such he and all his Catholic descendants were forfeit from the crowns, and both of his protestant daughters became queen. Once it became clear that neither Mary II nor Anne would have a child, the English parliament passed a law excluding Catholics from the throne. In response, Scotland passed a law underlining that the they had the right to choose their own successor to Anne, as like I said, the two thrones were not inexorable. This was a significant factor in England pushing for the Act of Union.

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But what happened to James? Well he maintained that he was King until his death, at which point it then passed onto the Catholic son, James Francis Edward, who claimed the throne as James VIII, and then onto his son, who would be Charles III. Charles Edward died without legitimate issue, so next it passed to his brother Henry Benedict.

However, at this point, the idea of a Jacobite claimant gets a little hairy. The Henry, who never officially referred to himself as Henry I, was a Cardinal, and as such definitely had no children to inherit the claim. Incidentally, by this point even the Papacy had given up on England and Scotland, and while they'd supported Charles III's claim, always referred to Henry as Duke of York, the title he was granted by his father.

So Henry dies with no son in 1807. Scotland hasn't existed as an independent nation for 100 years at this point, and both of his aunts are long dead, meaning the House of Stuart is now extinct. Jacobitism as a wide movement has not been a going concern for nearly half a century, the power of the Monarchy has been massively curbed by Parliament, and the laws of the United Kingdom now block Catholics from inheriting the throne. However, technically speaking the most senior claimant to the throne (ignoring James VII's line) after Anne's death was not George-Augustus of Hanover, but Anne Marie d'Orleans, Charles I's granddaughter, and wife of the King of Sicily. It is nine generations on from Anne Marie that we get to Franz, Duke of Bavaria.

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Sources:

Mitchison, R., Lordship to Patronage: Scotland, 1603-1745

Gestrich, A., The Hanoverian Succession: Dynastic Politics and Monarchical Culture

Harris, T., Revolution: The Great Crisis of the British Monarchy 1685–1720