Nope it's no longer a full node since peers can not download the full blockchain from you. However some, including core devs, will still refer to pruned nodes as full nodes. Since 0.12.0 and BIP130, blocks can be announced by header and pruned nodes can serve the blocks they have.
How much storage do you have available? Do you have over 2 GB?
Have you looked into running a pruned node? After initial launch of bitcoin core, close it and create a bitcoin.conf file with
prune = 550. https://bitcoin.org/en/release/v0.12.0#wallet-pruning
Also take into consideration of bandwidth usage. When I run nodes on a VPS I usually cut the bandwidth too. You can set these in your bitcoin.conf as well using
This way you can still have a fully functioning Bitcoin wallet but make it more affordable to run a VPS. Again it's not a full node, but it will have full functionality for running bitcoind on a server.