Yes most certainly possible.
There are numerous examples in Scriptures which even specifically say by doing what bad karma one gets birth in which animal (or insect or plants) yoni.
The following are only a few among such verses. From Manu Smriti:
12.62. For stealing grain (a man) becomes a rat, for
stealing yellow metal a Hamsa, for stealing water a Plava, for
stealing honey a stinging insect, for stealing milk a crow, for
stealing condiments a dog, for stealing clarified butter an ichneumon (mongoose);
12.63. For stealing meat a vulture, for stealing fat a cormorant, for stealing oil a winged animal (of the kind called) Tailapaka, for
stealing salt a cricket, for stealing sour milk a bird (of the kind
12.64. For stealing silk a partridge, for stealing linen a frog, for stealing cotton-cloth a crane, for stealing a cow an iguana, for
stealing molasses a flying-fox;
12.68. That man who has forcibly taken away any kind of property belonging to another, or who has eaten sacrificial food (of) which (no
portion) had been offered, inevitably becomes an animal.
Similarly, from Vishnu Smriti Chapter XLIV:
- Now after having suffered the torments inflicted in the hells, the evil-doers pass into animal bodies.
- Criminals in the highest degree enter the bodies of all plants successively.
- Mortal sinners enter the bodies of worms or insects.
- Minor offenders enter the bodies of birds.
- Criminals in the fourth degree enter the bodies of aquatic animals
Similarly, from Parashara Smriti we get the following verses:
16. If a woman despises her husband, because he being either poor, or
diseased, or a dunce, — she, after death, is born a bitch, or a sow,
again and again.
36. If a Brahman fattens himself with the food of a Shoodra polluted by the impurity of birth or death, I do not know what (vile) animals
he will be born (in subsequent lives)
37. Twelve times he will be born as a vulture ; ten times as a hog ; seven times as a dog ; this is what Manu has said.
56. The regenerate men who eat their meals, not having performed the rite for the Visvadevam, are born as crows; their food by no means
should be partaken.
55. When his hands exist, if a Brahman, wanting in knowledge, drinks water with his mouth plunged into it [like a beast], he surely shall
be born as a dog (in his next birth).