Legends
Absolutely; there are several examples of Force-sensitive animals in Legends materials.
The Jedi Path has a whole section devoted to this topic, titled (unsurprisingly) "Force-wielding animals". The list in that book includes:
Vornskrs:
Vornskrs are quadrupedal predators that can sense the Force and can use that sense to hone in on their prey. So because Jedi are strong in the Force, they appear as the biggest and tastiest meal a vornskr has ever encountered. Beware the enemy that utilizes this ability to hunt Jedi.
The Jedi Path: A Manual for Students of the Force
Ysalamiri:
Though vornskrs are organic "Jedi detectors," their Force abilities are negligible compared to those of the ysalamiri - arboreal lizards that create bubbles or voids in the Force that hide their energy from predators like vornskrs. Enough ysalamiri clustered together can generate a void large enough to disable an army of Jedi from using the Force.
The Jedi Path: A Manual for Students of the Force
Taozin:
Equally dangerous are the taozin, annelids the size of hovertrains found on the moon of Va'art. The nodules on a toazin carapace interfere with a Jedi'a Sense abilities, making the taozin appear invisible in the Force. This also applies to those who carry taozin nodules.
The Jedi Path: A Manual for Students of the Force
Nighthunters, or maalraas:
Also among the dangerous predators that use the Force are nighthunters, which have more in common with taozin than vornskrs. They can manipulate the Force to create a cloak of shadows around themselves.
The Jedi Path: A Manual for Students of the Force
Beck-tori:
Beck-tori are aquatic parasites from Nam Priax, but they can be found on many temperate ocean worlds. These creatures use the Force to enhance their senses to locate prey. They have also been known to use the Force to heal their injuries.
The Jedi Path: A Manual for Students of the Force
Akk dogs:
Akk dogs are commonly seen as Jedi pets or companions. I first encountered these animals on Ord Canfre's ExplorCorps outpost, but didn't think there was anything unusual about the bond they shared with their trainers. I discovered, however, that akk dogs will form a Force bond with any handler - Jedi or not - through an empathic link heightened by a rudimentary degree of telepathy.
The Jedi Path: A Manual for Students of the Force
Jakobeasts:
Jakobeasts are my favourite example of a Force adaptation. These arctic herd animals can use their horns to generate a telekinetic push. Enough of them can create a wave strong enough to flatten forests.
The Jedi Path: A Manual for Students of the Force
There's a margin note here from Thame Cerulian, Count Dooku's Jedi Master, which reads:
This is the truth! Flipped our speeder too! - Thame
The Jedi Path: A Manual for Students of the Force
In addition to those examples, Wookieepedia has several more:
Jubba birds, native to Dagobah, have a Force-assisted song:
The Jubba's most distinct feature was its unique hum, a soothing and eerie melodic whistle that calmed all but the most angry creatures and beings, and was a manifestation of the Force.
Marsh Haunts, a predatory species common on Mid- and Outer-Rim worlds, uses Force powers for hunting:
While non-sentient, they worked in loose packs of two to eight creatures to ambush prey, with some of them using their Force powers to scare potential prey toward the rest.
Muttamoks, introduced in the Star Wars RPG, appears to use the Force to communicate to a limited extent:
They were attracted to bright, shiny objects. A muttamok often went on the prowl for such objects, commonly resulting in thievery if needed. When captured by the item in question's owner, they could use an innate Force ability in a plea for sympathy.
Pelko bugs, native to Korriban, also use the Force to hunt, though unlike the Marsh Haunts they use it to determine what prey is worth attacking:
They lived only beneath sands of the Valley of the Dark Lords on Korriban, and were attracted to Force-sensitives. They would stalk and swarm their prey in the darkness. The bug's attunement to the Force allowed them to determine if a creature was suitable prey, as Darth Bane found when exploring the Valley, in which they found he was too powerful and did not attack.
Voxyn, a genetically modified hybrid of the vornskr, also hunt through the Force, and have some Force abilities as a result:
As they were made to kill Jedi, the voxyn could sense Force-sensitives through the Force and had a variety of deadly abilities and tools at their disposal: sonic blasts, flesh–melting acid, disease–coated claws, and a poisonous barbed tail.
As Omegacron reminds me in comments, Hssiss have the ability to become invisible, very probably by using a Force ability:
Hssiss also had the ability to conceal themselves and become invisible, possibly doing so through the Force.
Although it's not clear that the Terentatek can use any Force powers, they do appear sensitive to the Dark Side; it's said that they hibernate when the Dark Side is weak in the galaxy, and come out in Force when it resurges:
It was theorized that they were once rancors, subjected to mutations by the Sith, and that when the dark side was weak in the galaxy, terentatek would hibernate and remain dormant for many years, only to return when the dark side was strong again.
Canon
Nothing confirmed. Of the creatures I mentioned above only two, the Jubba bird and the Terentatek, have been introduced into the new canon. Unfortunately I'm not confident that the Force-sensitivity made the trip.
In the canon novel Dark Disciple, Quinlan Vos encounters the mysterious Sleeper of Dathomir, and speculates that it uses the Force to augment its sight:
[I]t was the kaleidoscope of colors that made the Sleeper so visibly remarkable. Every hue Vos could dream — or have nightmares of — adorned it. He had known other species to have eyes similar to the Sleeper's, which could see five or ten more colors than he could. But the Sleeper's eyes were even more complex, and Vos briefly wondered if this creature was so difficult to subdue because it might be able to actually see the Force.
Dark Disciple Chapter 17
However this is only a guess of Vos', and is never confirmed; the Sleeper is killed shortly after this, and doesn't appear in any other canon works.
