I heard it as "まるくなれますか" and I thought "Can we become round?", but then I started laughing. What does it really mean?
[Edit]
Sure, the full sentence was, something like this I think:
Ja, watashi mo Michan san to... maruku naremasu ka?
I think it's some sort of confession of love, but I'd like to know how a Japanese person would interpret that.
まるくなる
It usually depicts that a certain thing becomes round physically.
But, when we use まるくなる about a person, the meaning becomes different and is used as a figurative meaning.
It is a word expresses the human nature.
When you say 彼はまるくなった, it means he or his nature has become mellow, tolerant or gentle.
Also it is praise expressing he has grown up as an excellent adult.
Ja, watashi mo Michan san to... maruku naremasu ka?
After I read the sentence, I thought I had to add another interpretation to まるくなる.
It means "A becomes on friendly terms with B".
So the whole meaning of the sentence is like:
Then, can I also become on friendly terms with you, Michan-san?
I know "まるくなる with someone" doesn't mean "a person becomes on friendly terms with someone", which I wrote in my answer. As a matter of course, there is no such a meaning for まるくなる in Japanese. I inferred and answered this interpretation by examining the given phrase じゃあ、私もみっちゃんさんと...まるくなれますか？ So, the interpretation was totally my invention.
I searched for the phrase on the Internet, and at last I found it in an animated cartoon video. I'll show you the script at and after 8:21 from the beginning of the video as follows:
みっちゃんさん１： （8:21）ご機嫌斜めだね、夏目ちゃん。あれは傷つくよ～。あの年頃の男は繊細なんだから...
夏目１： 見てたんですか？みっちゃんさん
みっちゃんさん２： せっかく正月だし、はるの友達連れてきて、俺はうれしいし、夏目ちゃんやしずくちゃんにも会えてうれしいし、優しくしてあげようよ、ね。
夏目２： 別に、前ちょっといやな態度とっちゃって、どうすればいいかわかんなくなっちゃっただけです。
（なんだ普通にしゃべれる）
男の子嫌いです。特に私に言い寄ってくる男なんて大っ嫌いです。
みっちゃんさん３： あはーん、言うね。その年で男嫌いとは贅沢だね。俺は女の子が大好きだからね。
夏目３： みっちゃんさんも恋愛したいんですか。
みっちゃんさん４： （9:14）恋愛？ あははは～ なんせ借金が重くてね。でも恋はいいよ。恋は良くも悪くも人を変える。逆に言えば変わるチャンスだよね。（9:33）でえ、いい恋愛ってのは、人間をま～るくしてくれるんだよね。
夏目４： 私は、みってぃーや、はる君や大好きな人たちがいれば他はいらないです。そしてゆくゆくはみってぃー王国を。
みっちゃんさん５： ああ、いやいや。
夏目５： 誰も傷つかない。ずっと楽しい永遠の王国です。
みっちゃんさん６: ないよ、そんなのは。分かってるでしょ。
夏目６: （10:10）じゃあ、私もみっちゃんさんと...まるくなれますか？
In the line by みっちゃんさん４, there is a phrase いい恋愛ってのは、人間をま～るくしてくれるんだよね.
ま～るくなる in this phrase is まるくなる, and the meaning of it is to become mellow, tolerant or gentle what I wrote in my answer.
And, in the line by 夏目６, the exact phrase appears as was given by you or the questioner.
If you examine both phrases みっちゃんさん４ and 夏目６, it is easy to guess that 私もみっちゃんさんと...まるくなれますか？ means 私もみっちゃんさんと恋愛をして、まるくなれますか？.
Yes, she confessed her love to him by quoting from his former phrase cleverly.
