Not without voiding your warranty.
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It could be caused by your PSU too, don't rule that out. Find a game or application that produces the most whine and leave it running for 12-24 hours. This may soften the whine over time. If it's caused by the PSU, which is common, then the only solution is to try a different PSU. Some PSUs make GPUs whine.
One thing you could try is adjust the GPU voltage, power limit, and clocks. It's not guaranteed, but you may find some settings which cause less whine. And that won't void your warranty.