Currently to interact with Link in a fully decentralized way you need to have a fully syncronized node running locally. It can take a long time to sync and will take up a lot of storage space.
This will all change with Ethereum’s light client functionaity that is rapidly nearing maturity. Both Geth and Parity will be able to serve light clients and act as light clients themselves.
It will also be possible for Android and iOS devices to have light client functionality.