Is post-quantum Oblivious Transfer possible
Post-quantum oblivious transfer protocols are possible. If you base the security of the OT in a post-quantum assumption, this should give you an OT conjectured to be robust to quantum attackers. Besides the already mentioned OT based on supersingular isogeny (in comments), I can give you some other examples:

Code-based: https://eprint.iacr.org/2008/138.pdf , https://ieeexplore.ieee.org/document/6089575

Lattice-based: https://eprint.iacr.org/2018/530

There are also some constructions for OT ,secure in the Universally Composable framework and based on post-quantum assumptions, such as 

https://link.springer.com/chapter/10.1007/978-3-319-12280-9_10

based on the LPN assumption, and the ones that can be instantiated using the frameworks of: 

https://eprint.iacr.org/2007/348.pdf

and 

https://eprint.iacr.org/2017/993.pdf

using post-quantum encryption schemes.