There is / are; Questions > Answers; is > are ; are >is

It gets clearer if you write out the full response:

Are there any phones in the room?
Yes there is phones in the room.
No there isn't phones in the room.

So, if you answer strictly yes/no to the asker's question, you can now see that replying with "Yes there is..." to an "Are there any..." question is grammatically incorrect. The same goes for "Is there any..." questions; the pluralization in the response should match the pluralization in the question.

However, you can modify your reply if you want to imply something, such as in this case, how many phones can be found:

Are there any phones in the room?
Yes there is [a phone in the room].
Yes there are [several phones in the room].
No there aren't [any phones in the room].

As pointed out by user F.E. in the comments:

Your question actually involves two major issues:

(1) verb agreement in an existential construction,

(2) response to a question. Answer for #1, there is no need for verb agreement in an existential construction--even though grade schools and pop-grammarians push bogus "rules" at you. (The rule is: Trust your ear.)

For #2, often a person will respond to a question by sorta echoing part of the question back; so if the questioner began the question with "Are there", the responder might begin the response with "(Yes/no) there are"; and the same with "There is"--but it's up to the responder.