grammar - "I read the news on twitter that you asked me to" or "I read the news that you asked me to on twitter"

The sentence structure here is a little ambiguous. The preposition phrase on twitter could be postmodifying the noun news or it could be a modifier in the clause structure. As it happens, it doesn't matter for our purposes here, so I'm going to assume that it is postmodifying the noun.

Now the preposition phrase on twitter isn't the only modifier in the noun phrase. There is also a relative clause that you asked me to. Although there are a few constraints, what we generally find with post-modifiers in noun phrases is that the heavier (i.e. longer) phrases tend to come at the end and the shorter ones first. Whichever way round they are they will both be grammatical, but we tend to find sentences where the longer modifier comes second more natural and easy to process.

Here's an example:

• Have you heard the news on the tv about those terrible storms in the Pacific?


• Have you heard the news about those terrible storms in the Pacific on the tv? (awkward)

In the Original Poster's example, both modifiers are quite light, so either sentence is acceptable.