According to this article, it is possible.
Amazon’s own shopping app on iOS now allows you to give your
Amazon Echo voice commands through your phone, effectively getting rid
of the need for the $30 Voice Remote, too. It doesn’t directly control
your physical Amazon Echo unit, per se, but it acts as a virtual Echo
device, communicating with your Alexa account and letting you control
your smarthome devices by voice using Alexa on your phone.
The feature uses the existing microphone button in the app that’s used
for voice search. You can still use it for that, of course, but now
Alexa is completely built in.
Unfortunately, this feature is not yet available in the Android
version of the Amazon app, but luckily there’s a third-party app
(called Ubi) that gives you similar functionality.
From the Play Store:
This app requires that you have a valid Amazon account for sign in and
for accessing the Alexa Voice Service.
Supported features in this app:
Asking Alexa questions and getting a response
Controlling home automation devices
Accessing various Alexa Skills