All of the answers here are assuming that your English writing is in the passable category (for me, that would be C1 on this table, but some may argue that B2 is enough.) And if that is the right assumption, their advice is correct.
However, let me give you the contrarian view, from the perspective of an academic living in the US, and for whom English is his second language.
I get a lot of undergraduate and prospective graduate students who just don't have the language skills to communicate (A1 or A2). A lot of them seem to come with the idea that to get a degree all you need to do is to really want it and to believe in yourself. Well, neither is a pre-requisite for a degree, but English skills are. Just like any other pre-req for graduate school in Biology (my field.)
My first language is Spanish, but I split my time between Germany and the US. We speak German at home, but I would not even think of trying to get a job at a German-speaking workplace without some serious years studying the language until my writing skills were at C1. If only because in my experience, Germans are less forgiving when it comes to written communication.
Try to get an independent evaluation of your English writing skills. Or you could try a self-assessment, like this one from the Common European Framework of Reference for Languages (CEFR).
It could be that you are just suffering from impostor syndrome, have other anxieties regarding the prospects of doing a PhD, or have an unrealistic view of other people's writing skills. If that's the case, follow the advice from the other answers, accept the offer, and just work on your skills. But if you are seriously lacking, as in not being able to write a sentence without serious grammar issues, then you'd be well served by taking a year off and using that year to improve your skills. It can be done. I used to a have a recent immigrant as a student, and she did not speak a word of English. Two years later she was speaking and writing. Two years later she had a Master's degree. Last week I heard from her and she's finishing her PhD thesis at an R1 institution.