The Phaser is a 3x2 weapon room unlocked via the Fashionably Late (Supporter Pack). This pack can be bought by going to www.pixelstarships.com and paying $45 for it. The Phaser does 1 point of damage to crew and systems, and 0.5 points of damage to shields. This room has no correlation with the Plasma Phaser.
The Phaser is essentially a cheaper and less power consuming level one Plasma Phaser. What sets this room apart from the Plasma Phaser is its lower crew damage. Also, sometimes the bullet can hit a room but not deal damage. Finally, make sure to Armor the Phaser well as it can only take two System damage before hull damage occurs.
When To Use
The Phaser is pretty much only used in pure gunships, and even then it is uncommon. Most people can't find the space for this weak room in any other strategy. Nonetheless, if leftover space is available, the Phaser can certainly be used for extra DPS if more suitable options are lacking.
There really isn't any magic AI for the Phaser, just make sure it targets the same room all your other weapon rooms target. Also, the Phaser is categorized as a "Laser Room" in AI coding.
The Phaser is buffed with the Weapon stat on crew. The formula used with this stat can be found here.