ふりをする is an expression in Japanese that is used to show that someone is ‘pretending to be (A)’, ‘putting on airs of (A)’, or ‘acting as if (A)’. This construction comes from a combination of the noun 振（ふ）り ‘a shake’, the 副助詞（ふくじょし） (adverbial particle) を, and する. It can be thought of as meaning ‘to give off the impression of (A)’, or ‘to shake off the impression of (A)’.
As ふり itself is a noun, this expression may be used with the 連体形（れんたいけい） (attributive form) of any other word.

• この蛇（へび）は人（ひと）等（など）大（おお）きな動物（どうぶつ）が近（ちか）づくと死（し）んだ振（ふ）りをするらしい。
  I heard that this snake pretends to be dead when humans and bigger animals approach it.
• 僕（ぼく）は子供（こども）の頃（ころ）、よく寝（ね）ている振（ふ）りをした。
  When I was a child, I would often pretend to sleep.
• 欲（ほ）しいのはこれではなかったけど、せっかく買（か）ってくれたから嬉（うれ）しい振（ふ）りをする。
  This is not what I wanted, but since they went out of their way and bought it for me, I will pretend that I am happy.
• 俺（おれ）の前（まえ）ではそんな、元気（げんき）な振（ふ）りをしなくていいよ。
  You don't have to pretend that you are happy in front of me.
• カケル君（くん）はカエルが好（す）きだからいつもカエルの振（ふり）りをして遊（あそ）んでいる。
  Because Kakeru-kun likes frogs, he always pretends to be a frog when he plays.