Yes, but it doesn't quite mean the same as the given sentence (even if the two are usually translated the same way in English).
इस कमरे में राज खाता है। (~In this room, Raj eats) answers the question "Who eats in this room?" whereas राज इस कमरे में खाता है। is an answer to "In which room does Raj eat?"
So, a Hindi sentence usually begins with the topic (the known/given entity) followed by its attribute (a piece of information about the topic).
A sentence may not begin with the subject of the sentence if it isn't also the topic of the sentence.
In इस कमरे में राज खाता है।, the topic is यह कमरा and hence it begins the sentence. It's like saying "Talking about this room, Raj eats here". In cases like this, it might help to see the sentence structure as topic-attribute rather than subject-predicate.
It's used when you have prepositions like mein, paas, ke, kaa, ki, etc. (sorry for not writing in Hindi characters). You change the subject to which those prepositions refer to into oblique case (e.g. if you're saying "I have a cat", in Hindi that would be "Mere paas ek billi hai" (if "I" is a male), so here, mera has been transformed to the oblique form "mere" because "paas" is referring to mera).
Hope that makes sense!