It is possible to perform an in-place encryption but I would strongly suggest that you take a backup first. I wrote an experimental tool that I called inCrypt which can convert between raw (unencrypted), plain (dm-crypt) and LUKS formats.
Converting an unencrypted device to LUKS requires that any pre-existing data on the device needs to be shifted to leave a space of around 2MiB at the beginning so that a header can be installed there. Alternatively you can detach the header and store it on a separate device (such as a USB key).
If you use a detached LUKS header or choose plain-mode dm-crypt instead then there is no need to shift the data, it can be converted in-situ.
I wrote up the theory with examples here and you can also read about right-shifting and its inherent problems in this question.
To summarise, you can perform in-place encryption using dd to copy into a dm-crypt device mapper from the underlying raw device:
$ cryptsetup open "${raw_device}" crypt_device --type plain ${cryptsetup_args} $ dd if="${raw_device}" conv=notrunc of=/dev/mapper/crypt_device $ cryptsetup close crypt_device
(the variables are placeholders for you to supply the relevant parameters for your environment; it's more completely explained in the script and linked pages above)
This is a risky operation - if it fails part-way through (power loss, fat fingers, or for any other reason) then you are stuffed. Take a backup first.
Note that I used the words backup, experimental and theory. Caveat Emptor, and all that!