The Covenant, or petition, was dismissed by British Prime Minister Clement Atlee as an irrelevance, but it does survive to this day. Part of the petition is held by the National Records of Scotland under GD1/1215, with the catalogue entry noting that
Mr Ian Hamilton QC deposited this item with the Scottish Record Office (now the National Archives of Scotland) in April 1998. When first signed, the text had been hung on the wall of the Covenant Association Office in Glasgow and was accessible to the public. It was subsequently removed for safekeeping before being deposited in the SRO.
The rest of the Covenant - the overwhelming bulk of the petition - is held at the National Library of Scotland (www.nls.uk). Again the NRS catalogue entry states the following extraordinary story about its survival:
The main body of signatures, except the 160 on the first page, is now in the National Library of Scotland, Edinburgh (their ref: Acc5492). They are contained in thousands of separate sheets and were placed there in 1970 by Dr Winifred Ewing who had rescued them from a Rutherglen builder's yard.
The signing of covenants in Scotland, in recent history at least (the concept is actually biblical), goes back to 17th century Presbyterianism and the defiance of the population against Charles I's attempts to further introduce episcopacy into the Scottish church (his father, James VI, had already attempted to get things underway on that front). In genealogical terms, one such Solemn League and Covenant from 1912 has been fully digitised and made available online - signed by the Protestant population of Ulster and Ireland (and many worldwide countries, including Scotland and England), the descendants of Scottish and English planters who actually feared home rule for Ireland, the thought being that "Home Rule is Rome Rule". It can be searched and viewed online at http://www.proni.gov.uk/index/search_the_archives/ulster_covenant.htm.
The Diomhair (Secret) programme written by George Rosie for BBC Alba tells the extraordinary story of the Scottish Covenant movement of the 1940s (embedded here):
The 1912 Ulster Covenant signatures are online - what a great genealogical resource the 1949 Scottish Covenant signatures would be to see also.