Running a regularly updated blog and linking to it in your resume is a great way to do both.
You can pretty much write about anything that is related to your education, your programming skills, your choice of algorithms, and so on.
Don't worry too much about your writing style in the beginning and just keep posting. Once you write about 50 posts, you'll see that your writing style will improve a lot. In my example, I have started writing blog posts about a half of a year ago. Now, my writing skills have improved so much that my article is going to be published on Opensource.com during this week.
So basically, I've put in my resume the link to my personal blog alongside links to my online portfolio and my LinkedIn profile. The rest of my resume is now pretty much the same and I do have a way of showing my writing skills.
