The verbs arouse and rouse both mean (1) to awake from sleep and (2) to excite. But arouse is usually used figuratively or in reference to feelings, while rouse more commonly refers to physical action and things that inspire action. Also, arouse is more often used in relation to sex, and rouse more often relates to coming out of sleep.
These are not rules, however, and we could find many exceptions. For example, rousing is often used to describe works of art that induce strong enthusiasm, which is not a physical action. Using rouse this way is probably a smart choice, though, because describing a work of art as arousing might give the impression that the work is pornographic or otherwise erotic.
This being fairly transparent, it aroused strong feelings against Judge Goldstone. [National Post]
Around 150 passengers from two planes waited in the air as the pilots attempted to rouse the airport’s traffic controller. [Scotsman]
Everything about Perry is slickly packaged to arouse the prurient interest of heterosexual men. [AV Club]
Jakes threatened to rouse “thousands” into marches to oppose the “chaos” the proposal would bring. [Chicago Sun-Times]
Written in 1842, Verdi’s work is often credited with helping to arouse Italy’s national consciousness. [The Australian]