No, there is not.
This was posted as a feature request in 2012, and marked status-declined on meta.se:
Amongst the reasons for starting a bounty, one can select:
Reward existing answer
One or more of the answers is exemplary and worthy of an additional bounty.
Why not enable one to reward excellent questions in a similar manner?
SE staff animuson offers this explanation for declining the feature request, summarized in its first paragraph:
The problem with offering bounties on questions is it doesn't encourage any behavior from other users. When users see a bounty available on a question, it encourages them to provide a detailed answer in an effort to be rewarded the bounty. Even if you are "rewarding an existing answer" it is still possible that someone else may find something even more useful than the answer you originally wanted to give the bounty to, which is one of the reasons why the time limit still exists.
Bounties are for answers and should only be used for answers.
The bounty system is designed for encouraging a particular type of engagement: answers to questions. This is what it is for, and this is what it should be used for (more on the intent behind the design of the bounty system can be found in animuson’s meta post linked in the previous section). Using the bounty system to “gift reputation” for anything other than bounty-worthy answers is reputation that the recipient did not earn, since it is reputation gained via unintended methods. Now, if the recipient already has 25k reputation this isn’t that big of a deal, but below 25k rep, site privileges are locked behind reputation thresholds, and I’d really prefer reputation thresholds be met by gaining rep the intended way.
That said, if you still really want to award a particular user for a great question, go find a bounty-worthy answer of theirs. But please be sure it’s actually bounty-worthy. We can’t read your mind, and this works on the honor-system, but we will know something is up if you award a bounty to a clearly low-quality post.