No, unfortunately you cannot take the Duolingo test on your phone.
You can find a list of compatible devices at this link: https://testcenter.zendesk.com/hc/en-us/articles/5297715242125-What-devices-and-operating-systems-can-I-use-to-take-the-Duolingo-English-Test-
If you do not have a laptop or computer, please ask a friend or family member if you can borrow one for your Duolingo test.
If you cannot borrow a computer, please send an email to applications@sye-initiative.org explaining your situation. Include the words "Duolingo device" in the subject line of your email.