As Shimrod said, there are two incomplete versions from traditional Traveller singers, Betsy Johnston and Willie Whyte (notes below) and a few verses were collectd by Hugh Shields in the 1970s, from Northern Ireland singer Eddie Butcher.
"As I understand it, "Tam Lin" began as a ballad in its familiar form some time in the 18th Century."      
With respect, as we have little knowledge of what existed in the tradition prior to the end of the 19th century, so we have no idea whether the ballad existed, or, if it did, in what form in the 18th century, we only know what went into print, which is no guide at all.
Jim Carroll

"Camped in the berryfields of Blairgowrie in the summer of 1956, and talking to many families of travelling people who were camped there too, I had plenty of opportunities of veri¬fying that belief in fairies, fear of abduction by fairies and all manner of taboos rooted in supernatural folklore were still living concepts among them. This naturally led me to ask for Tam Lin, and it soon became clear that there were people known to the campers who sang it. A young Johnston camped at the Standing Stones who told me a number of Marchen gave me an address in Dumbarton which he said might lead me to folk who could sing the ballad. Unluckily I had neither the time nor the funds to follow up this lead immediately, and when I did get to the address in question, I found that the family had done a moonlight flit, and there was no trace of them. All that a neighbour could tell me was that one of them was in Barlinnie prison in Glasgow, doing time for some trifling misdemeanour, so I resolved to try and contact him. A phone call to Barlinnie seemed to be a forlorn hope, but I made one all the same, and luckily got in touch with a sympathetic official. To him I dictated a message, couched partly in cant (the travellers' cover lingo), explaining who I was and what I wanted. The official told me to ring again in half an hour. When I did so, I was given an address in Risk Street in Glasgow. This turned out to be a "half way house", but within an hour of the second phone call to Barlinnie I had tracked the family down to its temporary home in Ancroft Street, and was recording "Tam Lin" from Betsy Johnston.
This was a moment to remember, like the first time I heard Jeanne Robertson launch into The Battle of Harlaw. With the first notes of "...Lady Margaret", which seemed to come 'seeping through the branches' of Chaster's Wood (or Carter-haugh), one was aware that one was in the presence of an immensely long unbroken oral tradition. Tarn Lin, on the lips of this stravaiging singer, provided instant evidence that the ballad had been travelling around for centuries in the care of these nomadic Johnstons, who were living out elemental ballad themes in South-West Scotland long before Robert Burns was born.
In addition, Betsy's version seemed to put into perspective the magnificent Tarn Lin which Burns sent to James Johnston for inclusion in The Scots Musical Museum-a version which is still (with Lord Hailes's Edward and a handful of others) one of the most famous ballad texts in the world. Burns drew on orally transmitted variants from the Borders and the South-West, but he tightened up the narrative and turned the ballad into a poem which reads supremely well on the printed page. In so doing he appears at one and the same time as a great art-poet, an 18th century-style collector, and a 'folk poet writ large'.

Willie Whyte, a well known figure among the Aberdeen tra¬vellers, was one of the links in the chain which led me to Jeannie Robertson.
There is some ambiguity as to the mode of Betsy Johnstone's tune; much depends on whether her last note is considered to be the key-note or tonal centre of the whole. If one decides it is - and my impression of the tune supports this decision -then it follows that the air is closer to the Lydian (a rare mode in Scottish tunes) than to any other. The musical significance of the sharpened fourth here does not depend on its total duration nor on whether it is accented; the question is more subtle and elusive. Many a ballad tune will shift its tonal centre at least once, and here the fourth line's ending on the sixth of the scale may be heard as a fleeting reference to the Dorian mode, which is the relative minor of the major-mode Lydian.
Betsy's fine tune is given - as an example of the Lydian -in Francis Collinson's The Traditional and National Music of Scotland (p. 16), but neither this nor Willie Whyte's tune is in Bronson.
Betsy's performance of this powerful and haunting ballad is intensely rhythmic (you can hear the tapping of her foot occa-sionally), yet paradoxically it sounds untrammelled, free of all save her own inner consciousness of that pulse which is part of nature itself. Betsy's resonant voice increases the song's impact, and she uses occasional fleeting yet effective ornamentation of the mordent type.
Willie Whyte's version settles, after the first line, into some¬thing very close to Sheila MacGregor's tune for The Twa Brothers. His unashamedly flamboyant, emotional and more ornamented rendering provides an interesting contrast and complement to Betsy's."