Yes there's a few ways you can make money writing articles online.
You can start a hubpages account and write articles and if they're good enough they can earn you some money eventually through Adsense or affiliate programs.
It can take a few years to earn good money through hubpages though so it's not quick money.
If you want to make quick money writing articles try going to freelancer and looking for freelance jobs where people will pay you the freelancer money to write articles for their website or blog.
You could also create your own website or blog and write articles for your own blog which will eventually bring you money through affiliate programs or Adsense as well.
If you go for hubpages or your own blog expect the money to be nonexistent for a few years.
Unless you're lucky it can take a good few years to start seeing enough website traffic to your blog to earn a living with.