From James C. Dick's The Songs of Robert Burns (1903, p. 461):

No. 277. When first my brave Johnie lad. Scots Musical Museum, 1792, No. 309., entitled Cock up your beaver. The MS., not in Burns's hand, is in the British Museum. A fragment of the old song is in Herd's Scots Songs, 1769, 314. Burns made a few alterations in the. first stanza, the second being entirely his.
The tune was popular in England as a Scotch dance in the seventeenth century. It is printed in the seventh edition of Playford's Dancing Master, 1686, also edition 1695, entitled Johnny cock thy beaver. It is also in Atkinson's MS., 1694; in Durfey's Pills, 1719, i. 332, set to a semi-political song beginning 'To horse brave boys of Newmarket, to horse'; in Sinkler's MS., Glasgow, 1710; in Oswald's Companion, c. 1755, vii. 2; and in McGibbon's Scots Tunes, 1755, 20.