It would depend on whether the child was registered in it's mothers name or adoptive parents. Might be worth looking for it on Scotlands People
http://www.scotlandspeople.gov.uk/welcome.aspxUse the year and mother's surname leaving the first name blank select Edinburgh and the area of the mother and baby home within Edinburgh.
Statutory adoption did not become legal until 1927 so with a bit of luck ........
Good luck!

ps
If you were adopted in Scotland:
Records can be obtained from the General Register Office for Scotland.
Records are available at the Adoption Unit at New Register House
Contact the General Register Office for Scotland:
New Register House
Edinburgh
Eh1 3YT
Telephone: 0131 334 0380
Email: records[at]gro-scotland.gov.uk
Website:
www.gro-scotland.gov.ukModerator Comment: e-mail edited, to avoid spamming and other abuses.
Please replace [-- at --] with @