The bones were primarily from cows, pigs, sheep and deer in the earliest uses, with cattle and water buffalo bones being the most common. We're talking Neolithic times here. There's still some uncertainty with exactly what species some of the bovine bones belonged to, but we know they're bovine.

However, human bones were used for inscriptions, but not for the more religious/divination purposes. Quoting here from Chapter 1 The Divination Materials of Keightley's Sources of Shang History on the oracle bones:

The cranium, astragalus (ankle bone), and ribs of these bovids were also occasionally divined at An-yang, but such bones were primarily used for practice inscriptions or record keeping. Human and deer skulls were also inscribed with records, as were other bones from deer and horses, but with the exception of one horse scapula, they do not appear to have been used for pyromancy. Most of the non-divination writings on bone are records of hunt or sacrifice from period V, often given with a Shang date, and may have been carved on the bone of the animal or human victim.

Later on, people started using turtle shells as well, which are some of the more common cases of the oracle bone inscriptions that are around today.

The answer is both yes and no. Yes human bones were inscribed on to some extent, but no it wasn't for the same purposes of divination that the oracle bones are really known for.

tl;dr: Yes, but also no.