Yes. It is totally proper and ethical, as long as you are one of the main person/people who understand well the work.
Indeed, almost all my publications during my graduate student time to obtain a PhD, I am the corresponding author for almost all these papers (around 1010+ papers).
In reality, you do not even need to be a graduate student in PhD to be the corresponding author. There are both undergrads and amateurs who are the leading and the corresponding authors for their papers.
It is fairly common in my PhD institution to do so.
(p.s. My PhD institution is Massachusetts Institute of Technology.)