A college plagiarism charge can definitely hurt your chances of getting into grad school. The unfortunate reality of it is, is that any kind of handicap or black mark on a college student's record, disciplinary record, is going to negatively impact their prospect of getting into graduate school. If a graduate school has, say, for example, 20 available slots for incoming students and 100 people apply to equally competitive applicants, any academic misconduct charges aside, the school's going to choose a student that doesn't have say, an academic misconduct finding in almost all instances. That's the unfortunate reality.
If you're accused of plagiarism at college, it is incredibly serious, it can have both short and long-term consequences. It really depends on the nature of the plagiarism. Was it intentional? Was it unintentional? Was it self-plagiarism? Many schools do not distinguish between unintentional plagiarism, a student potentially not being culpable for that, but was it a misunderstanding between the professor's instructions and the student's obligations? Was the professor unclear? Did the student in fact, properly cite? Are you being accused because for example, the professor or the school used a plagiarism checker, and they turned up in an erroneous result or an incorrect result, in other words, and the school's basing the allegation on those results?
You have to take the necessary precautions before you engage with the school in any capacity. Having an experienced academic misconduct attorney advisor is going to be your best ally in terms of understanding and navigating the process. They should be involved as early as possible in an academic misconduct case.