Nope. But this "nope" needs a bit of qualification. Two things:
a. Repentance and belief only is needed to be "qualified" for Christ's church.
b. Water baptism is an sign and seal of the promise, and on our part a public acknowledgment of ~ and even a call on God's promise and absolute trust in His ability to bring His good work in the person to completion at the day of Christ, thereby delivering him/her to glory. This point needs a bit of clarification also:
* Peter says to the men of Israel that the promise is for them and their children. He does not specify an any age requirement, and it is a surety that many men in Peter's hearing had babies in their households. So this water baptism can be administered to babies, also, as the promise is for them, too. Water baptism has taken the place, in the New Testament church, of circumcision, which was to be done on babies eight days old (full immersion not necessary, but sprinkling, the Biblical precedent being what God says about the spiritual baptism that He Himself administers in Ezekiel 36:25 ~ "I will sprinkle clean water on you, and you shall be clean from all your uncleannesses..."). In the case of infant baptism, it's really about the parents' public acknowledgment of and call on God's promise to convert the baby's heart at the time of His choosing and absolute trust in His ability to bring His good work in the baby to completion at the day of Christ, thereby delivering him/her to glory.
So while water baptism is not a requirement, it is... strongly urged, for several reasons.
And actually, to put it another way, it is more correct to say
everyone is "qualified" ~ 'eligible' is more accurate ~ because in a very real sense,
no one ~ in his or her natural state ~ is qualified. :) It
depends on God's mercy (Romans 9:16) to
declare a person qualified... to baptize the person with water and the Spirit (John 3:5) and to justify him/her (Romans 8:30) by imputing the righteousness of Christ Jesus upon him/her and this give him/her new life by His Spirit (John 3:6)... to place him/her in Christ (Romans 8:1).
Grace and peace to all.