Your job as Rook is to hold lanes and deal quick bursts of damage in group fights. You're a tank in terms of hitpoints, but don't forget that you have incredibly low armor. The longer a game goes on, the stronger you are going to become. You must always be cautious as a rook player, and communication with your teammates is a must for survival.
Level 1: Power of the Tower I
Level 2: Archer Tower
Level 3: Save
Level 4: Power of the Tower II
Level 5: Boulder Roll And Tower of Light
Level 6: Hammer Slam I
Level 7: Power of the Tower III
Level 8: Trebuchet
Level 9: Hammer Slam II
Level 10: Power of the Tower IV
Level 11: Boulder Roll II
Level 12: Hammer Slam III
Level 13: Hammer Slam IV
Level 14: Save
Level 15: Dizzying Force and Boulder Roll III
Level 16: God Strength I
Level 17: God Strength II
Level 18: God Strength III
Level 19: Poisoned Arrows
Level 20: Stats
Nothing special here.
Favor: Blood of the fallen, staff of renewal, or dark crimson vial
Start with scaled helm and banded armor. On your first trip back, buy vlemish faceguard and a teleport scroll if you can afford it.
Next, buy unbreakable boots followed by nimoth chest armor. When the money is available, switch out scaled helm and banded armor for a plenor battlecrown and eventually a narmoth's ring or If you want to get some kills or are having trouble escaping, buy the wand of speed. If you have tons of cash even after upgrading the citadel, go for an orb of defiance and use it to burn through the cooldown of an enemy's sigil, or when your allies need time to get to you.
Whenever possible, try to buy fortified structures I, experience I, and creep upgrades. (don't buy priests too early though). Buy teleport scrolls, sigils, and capture locks as needed.
Dark Crimson Vial
This is a very good favor item if you're an aggressive rook player. If you take DCV, I suggest that you push your lane partner really hard and try to force them to shop so you can take down a tower before FS1. I suggest hammer slam at level 3 when using this favor item so that you can nuke the tower while killing a creep wave and keep pushing hard.
If you have an unclean beast, I would cede the mana flag to him on cataract. An over-leveled rook is almost as intimidating as an unclean beast, and he's more of a gank machine than he's given credit for.
Try to save mana for boulder rolls and encourage your teammates to frequently port in when you can get a kill.
Remember that kills are not the most important thing in the game, but they will give you money, and more importantly, they will let you farm warscore, gold, and experience while you knock down towers.
On cataract, you can safely put pressure on the enemy's mana flag if you so wish by placing your towers in a line.
Don't let any flag go yellow unless you feel you can capture it completely because your enemies will get experience if you only cap it half way and then back off, don't forget it.
What you can do is pin them to their portal with your tower farm denying them gold and experience if they are far enough away from the creep wave.