Can the setter attack the ball in volleyball?

Yes. A front-row setter may attack (dump) on the second contact from anywhere in the front zone. A back-row setter may not attack above net height from in front of the 3-meter attack line.

Full Explanation

The setter is not prohibited from attacking by any special rule. When the setter is in the front row, they may use any legal attack hit (including a tip, roll shot, or hard swing) on the second contact, commonly called a "setter dump" (FIVB Rule 13). When the setter is in the back row, back-row attack rules apply (FIVB Rule 13.3.2): the setter may not attack above net height if the takeoff was from at or in front of the attack line. A back-row setter may tip or roll the ball below net height from any position. All contact rules (no lifts or doubles, FIVB Rules 9.2.1 and 9.2.2) apply to the setter's attack just as to any other player.

Rulesets covered: FIVB/USAV/NFHS/NCAA  |  Rule Reference: FIVB Rule 13; FIVB Rule 13.3.2