Yes. Internet cafés often have fax machines, and some hotels may have business centers with fax machines as well.
Can I Use My Cell Phone in Ecuador?
How Long Will It Take a Postcard To Reach the U.S. in Ecuador?
What is Ecuador's Time Zone?
What Are Other International Calling Codes in Ecuador?
How Do I Dial from Ecuador To the U.S.?
How Do I Dial From the U.S. to Ecuador?
What is Internet Access Like in Ecuador?