In the following:
Registration of Births, Deaths, and Marriages (Scotland) Act 1860 23 & 24 Vict. c. 85
6 August 1860
There is explicit reference to Petitioning the Registrar-General by warrant viz.
"Register of Neglected Entries.
II. It shall be competent for any Person on Payment of a Fee of Five Shillings to register in a Book to be kept for the Purpose in the General Registry Office, to be called "The Register of Neglected Entries," any Birth, Death, or Marriage which shall have taken place in Scotland between the Thirty-first Day of December One thousand eight hundred and the First Day of January One thousand eight hundred and fifty-five: Provided always, that in order to such Registration there shall be produced to the Registrar General a Warrant to that Effect by the Sheriff of the County in which such Birth, Death, or Marriage occurred, to be granted upon a Petition, of which Intimation, by Advertisement or otherwise, shall be made as such Sheriff may direct, and after due Inquiry, and hearing any Parties having Interest who may appear to oppose such Petition, and which Warrant, and all written Documents produced to such Sheriff, together with his Notes, which such Sheriff is hereby required to take, of all parole Evidence adduced before him, shall be transmitted to the Registrar General, and shall be retained among the Records of his Office: Provided also, that a Copy of the Entry of any neglected Birth, Death, or Marriage which occurred subsequent to the Year One thousand eight hundred and nineteen shall be made and transmitted from the General Registry Office to the Registrar of the Parish or District in which such neglected Birth, Death, or Marriage occurred, and shall by him be recorded in such Form and Manner as the Registrar General may direct."
This act has been superseded but presumably the same mechanism of petition exists in later revisions i.e. not just for the period mentioned above.
Searching the National Records of Scotland catalogue returns three such petitions raised via the Court of Sessions all at more recent dates than 1868.
S_L