I am not sure if I am understanding the question. Can cremation remains be radiocarbon dated, then yes they can. If you are asking if we can determine at what point the remains were cremated, as in that they were within a vault or charnel house for years and then cremated, then the answer is very likely no. If there were small bones that fell outside the crematory fire and were not consumed, then one possibly could extract a different date. However, RC dating is not that precise, regardless of what television programs and movies make it out to be. In a several hundred year old sample there might be a +- of 15 to 60 years or so, while something several thousand years old might give a +- of 150 to 600 years or so. Many tens of thousands of years old remains can yield +- ranges in the thousands of years. Normally, the stage between death and cremation is no more than a few years.
For more on the process per one of the world leading labs see the Sample Type and Radiocarbon Dating headers at http://www.radiocarbon.com/
At the best of my knowledge, if you radiocarbon date human remains (after cremation), what you are actually dating is not the cremation itself, but the "moment" in which the organic material ceased to absorb athmospheric carbon. And provided that, as James a Green stresses, the cremation is very close to the death, the dated event (i.e., the death of the person) and the target event you are interested in (i.e., the cremation itself) would be so close in time to be "practically" coeval.
Yes, radiocarbon dating of burned skeletal remains is routine procedure nowadays. It is a bit different than conventional radiocarbon dating since it targets the structural carbonate of the mineral fraction rather than the organic fraction. However, it works better (if not exclusively) on completely calcined remains (usually burned at temperatures higher than 700/800º C). This is to make sure that no organics are left on the bones.
Here's some bibliography on that matter:
Lanting JN, Aerts-Bijma AT, and Plicht Jvd. 2001. Dating of cremated bones. Radiocarbon 43(2A):249-254.
Olsen J, Heinemeier J, Bennike P, Krause C, Hornstrup KM, and Thrane H. 2008. Characterisation and blind testing of radiocarbon dating of cremated bone. Journal of Archaeological Science 35:791-800.
Van Strydonck et al. 2005. 14C-dating of cremaed bones, why does it work. Lunula Archaeologia Protohistorica XII: 3-10
Stefan Ziemendorff- in straight way you wanted to know when the practice of Cremation started. Burial practice has been the very ancient way of disposal of the dead known since Palaeolithic time. But, cremating the dead seems to be not not very ancient cultural practice. The Happans of 5000-3000 B.P used to bury the dead. In some case Cremation has been suspected during the Bronze Age at Mohen-jo-Daro or in several Late Harappan sites of 3500-2500 BP, when we see partial burial or a secondary burial representing a few buried parts as the major body has been cremated.
It is funny how different people read a question differently. I read the question once again after your answer and saw that he was asking about how old was the practice.
While dated, Clark and Piggot (Prehistoric Societies, 1965:309) note that during the Bronze age ca. 1500 BC in the British Isles there was a "universal adoption of cremation as a burial rite." Braidwood (Prehistoric Men, 1975:190) says that cremation burials began in Britain ca. 1400+ BC and cremation burials in funeral urns was practiced across the island by ca. 1200+ BC.
Do you have any ceramic artefacts associated to the remains, i.e that accompanied them during the cremation? Thermoluminescence may be a good option as long as the burning attained high temperatures (it should be alright if bones are calcined). Also, the cremation must be rather ancient (> 1000 years) to allow for a reliable dating.
As David rightly pointed out, thermoluminescence would probably be the best option for dating the moment of cremation (instead of the moment of death, as C14 would).
Nevertheless, one must also bear in mind that TL dating tends to result in quite large intervals. So, depending upon the context you're analysing, it may or may not be useful. Notably, if you intend on obtaining fine-resolution results, it can come a bit short as a useful method.
The linked article may further help with this issue.
cremation was practiced in Ireland since at least the early Mesolithic - almost 10,000 years ago. Little, A., Van Gijn, A., Collins, T., Cooney, G., Elliott, B., Gilhooly, B., . . . Warren, G. (2017). Stone Dead: Uncovering Early Mesolithic Mortuary Rites, Hermitage, Ireland. Cambridge Archaeological Journal, 27(2), 223-243. doi:10.1017/S0959774316000536
As to radiocarbon dating cremated bone- as others pointed out it is of course possible but there is a concern about old wood effect....