gerbil

The word for gerbil, the small rodent, has Semitic origins:

1849, gerbile, from French gerbille, from Modern Latin Gerbillus, the genus name, from gerbo, from Arabic yarbu. Earlier English form, jarbuah (1660s), was directly from Arabic.

Another rodent that I hadn't heard of before also gets its name from the same Arabic word - the jerboa. They aren't from the same genus or even family, but because both are small desert rodents, the Arabic name was also used:

small desert rodent, 1660s, Modern Latin, from Arabic jarbu "flesh of the loins," also the name of a small jumping rodent of North Africa. So called for the strong muscles of its hind legs.

The Arabic Etymological Dictionary finds cognates in other Semitic languages:

yarbu‘ : a rodent, jerboa [Akkadian arrabu, Syriac yarbu‘a, Ebla arrabu]

Is there also a connection to any Hebrew words? 

One possibility is that it's related to akhbar עכבר - "mouse." We discussed akhbar a few years ago, relying on the theory that it derives from the root כבר - "great." Those that connect yarbu to akhbar take a different route. I found that theory mentioned here, here, and here. While they don't map it out directly, my understanding is that the "kh/k" sound dropped out (perhaps easier to imagine knowing that it was also pronounced/spelled agbaru in Akkadian, since the g sound gets swallowed in the b sound), and then through metathesis it became arrabu. 

And while the Online Etymology Dictionary says the name of the rodent came from the strong leg muscles, the first source (an essay by Prof. Richard Steiner) posits that the root first meant "mouse" and then later meant "muscle," particularly the Achilles tendon, or hamstring. He points out that in other languages we also find the word for muscles deriving from the word for mouse, including English:

"contractible animal tissue consisting of bundles of fibers," late 14c., "a muscle of the body," from Latin musculus "a muscle," literally "a little mouse," diminutive of mus "mouse".

So called because the shape and movement of some muscles (notably biceps) were thought to resemble mice. The analogy was made in Greek, too, where mys is both "mouse" and "muscle," and its combining form gives the medical prefix myo-. Compare also Old Church Slavonic mysi "mouse," mysica "arm;" German Maus "mouse; muscle," Arabic 'adalah "muscle," 'adal "field mouse;" Cornish logodenfer "calf of the leg," literally "mouse of the leg." 

Steiner then goes on to suggest that other Hebrew words for muscle might derive from the same root, including ekev עקב - "heel" and arkuv ערקוב - "knee joint, hock."

There is another small rodent, which like the gerbil, is often kept as a pet - the hamster. The word hamster doesn't have a Semitic etymology, but the hamsters we're familiar with today do have a connection to Israel. In 1930 in Jerusalem, the zoologist Israel Aharoni successfully bred a pair of Syrian hamsters, and the hamster pets found today worldwide are descendants of his efforts.