Domain name redirections on the DNS level are possible only by using CNAME records. Though in this case it is possible to redirect only subdomains. 

For more information on how to set CNAME records for your account please check this link.

The other option, provided you have hosting accounts for both domains, is to make the redirect using files. More information on how to do this can be found in these two articles:

PHP and HTML redirects

Creating redirects through cPanel

If you are having problems using redirects at your current host, you can sign up for our cPanel hosting package. SiteGround's support team will happily assist you with any domain redirects you request.