Both are correct, and in different parts of the world you'll hear both being used. 

However, I use "There's no need to call. Just text me" far more frequently. 

I agree with the thus stated. Yet 'me' also stands as a strong 'understood' and could easily be removed entirely from the set of both statements, which can additionally be employed as one sentence, i.e. "There's no need to call - just text." or "There's no need to call; just text." etcetera.

You don't need the 'me' after 'call'. The verb 'call' and its synonyms (phone, telephone, ring) don't need an object. Just phone. Just ring.

I'd say this without the 'me' to avoid the repetition: "There's no need to call. Just text me"

Hi Kharma, both optiones are correct. Although I'd prefer the first one so you don't repeat the word "me". But you can use both of the optiones you have there :)

you can text me instead of calling , actually the verb text is new ver ,,so you can't consider it grammatically 100% true