It's definitely an interesting idea.
It may be more natural to compare to the situation where you have the same tax level but it's going to the government, rather than the case where the you have less tax. That way we don't have to consider the welfare or incentive effects of changing the tax rate.
Advantages compared to general taxation:
- May be easier to build support for
- Allows targeting of very high-value opportunities
Disadvantages compared to general taxation:
- Money gets distributed according to what sounds good
- Encourages people to give to charities that benefit them
I think this last could be a big one. If this tax were in place I'd expect to see a lot more money going to services (art galleries etc.) providing public goods in rich neighbourhoods.
The penultimate one could also be a problem. At least in the UK, government spending is meant to go past cost-benefit analysis. This keeps it doing a reasonable job of funding effective things and skipping ineffective things. This tax looks better the worse-run government spending is.
Even with good government spending it could end up having a beneficial effect if it increased the proportion of money spent on international aid. I'm not sure whether we should expect that.
This would create an additional (and large) incentive for people to funnel their money through faux-charities, and to create faux-charities that'll circuitously direct it back into the pockets of the donors, either fraudulently or legally, like Owen_Cotton-Barratt said.
There are responses you could make to this (watchdog organizations that monitor the effectiveness of various charities and governmental authority, tighter laws regarding charitable incorporation) but so far as I can see they're all subject to the principal-agent problem.
Other than that I like the idea.