char is an integral type, so you can use it as a simple integer:
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int arr[10];
for (char i = 0; i < 10; ++i)
std::cin >> arr[i];
Or you can use it in character context in body of the loop:
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for(char c = '0'; c <= '9'; ++c)
std::cout << c << '\n';
Please note, that you are likely to have the expected results when iterating for example from a to z, it is not actually set in stone, so computers using some obscure codepage can produce unexpected results.