There didn’t use to be; the House of Commons Research Briefing, Leadership elections: Conservative Party notes that in the first ballot of the 2001 leadership election, David Davis and Michael Ancram tied for last place with 21 votes each. There had been no provision for a tie in the rules, so all five candidates advanced to the next round of voting, and no one was eliminated.
It further explains:-
Subsequent rules have made provision for a tie. In the first instance, the ballot is re-run. If there is again a tie among candidates with the least votes, those candidates are eliminated. However, if only three candidates are involved in the ballot, the ballot is re-run until only one candidate has the least number of votes.
Because the exact rules governing the leadership contest are not made publicly available in full by the 1922 committee, I can’t quote the exact rule for this year’s contest, but it seems very likely that the above rule is in place, and the ballot would be re-run until one candidate could be eliminated.