I've no idea of the exact number, but here's a few:-
Arthur James Balfour 1902-1906
Henry Campbell-Bannerman 1906-1908
Andrew Bonar-Law
James Ramsey MacDonald
**Alexander Douglas Home had Scottish ancestry but was born in London, so he probably doesn't count.
the recurring inability of the English to run their own country is a bit of a mystery, isn't it... Just as well the Scots are prepared to shoulder the burden for them while the locals sit back and moan about it.
Eight in total and all of them are covered by answers above. (Depends on your definition of 'Scots', of course, as New Yorker's reference to Sir Alec Douglas-Home above makes clear. As he was heir to a Scottish earldom, I think it is right that he should be considered a Scot despite having been born in London. The same is true of Bonar Law...born in Canada, as Kempie points out... and the Earl of Bute, also London-born.)