The US already had a ban against paying for international abortions. This is a ban of funding organisations that even talk about abortions, even if the US funding isn't related to abortions.
(I also disagree with your point from an ethical point of view, but that's not relevant here.)
He literally already has signed an executive order about it.
'Donald Trump has signed an executive order to ban federal money going to international groups which perform or provide information on abortions.
'The US president's order shows he "wants to stand up for all Americans, including the unborn," his press secretary Sean Spicer said.'
http://www.bbc.co.uk/news/world-us-canada-38724063