Diana Gabaldon has resurrected an interest in the Jacobite cause. This was an important part of Scottish history which found the Jacobite sympathisers aiming to restore the Roman Catholic Stuart King (James VII of Scotland & II of England) and his heirs to the throne. James had been replaced on the throne by his daughter Mary II and her husband, William of Orange (William III).
The Jacobites believed that being King was a God given right and passed on through heredity and were opposed to parliamentary interference with the line of succession to the throne. They saw this interference as being illegal.
People were expected to swear allegiance to their King and his authority. Jacobites wouldn't swear allegiance since William was not a direct descendant of James, while Charles Stuart (Bonnie Prince Charlie) was. Hoping to reinstate the Stuart regime, the Jacobites rose in rebellion on a number of occasions, notably in 1715 and in 1745.
Beginning in 1716, Jacobites were rounded up, imprisoned and subsequently transported to the Americas. Approximately 1,500 Jacobite prisoners were exiled to the American Plantations.
There are extensive resources to consult if you think your ancestor may have been involved with the Jacobite rebellions/risings. Few, however, are online.
The National Archives in London has a list of Jacobite Prisoners Following the Battle of Culloden: http://www.nationalarchives.gov.uk/education/resources/jacobite-1745/prisoners-after-culloden/
The National Archives also has a record of some of the trials in which the Jacobites were tried for treason: http://www.nationalarchives.gov.uk/help-with-your-research/research-guides/jacobite-risings-1715-and-1745/#6-trials
An interesting booklet on the Jacobites who were in Scotland, Ireland, and then in many cases onto America and which might help you link your Scots-Irish ancestor back to Scotland:
Frances McDonnell, Jacobites of 1715 & 1745. North East Scotland, Genealogical Publishing, 2000, Reference, 96 pages.
There are two other books in the series, specific to Perthshire and the Highlands.
A list of Bonnie Prince Charlie's Muster Roll is in this very comprehensive book:
Christian Aikman, The Muster Roll of Prince Charles Edward Stuart's Army 1745-46, Neil Wilson Publishing, 2012, 310 pages
Online searches can be done on the following websites: http://www.jacobites.net/jacobite-trials.html
PDF listings of Jacobite prisoners for various regions of Scotland can be found here: http://www.jacobites.net/lists.html
Best of luck researching your Jacobite ancestors.