"For such a time as this ...." is ok. I would tend to say, "For such a time like this ..." myself, or even abbreviate it further and say "For a time like this ..."

Yes i think the most people utilize this phrase ( for such time like this )

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I will use it in a graduate school application essay, which I assume somewhat formal and literary.

How are you using this phrase? It seems to me that it would be more literary, and I would not use it just to say "For now I'm staying here," or "This will do for now," or "Hey, thanks for book, it's just what I needed." Also, the phrase could be found in many older or more formal texts, not just the Bible.