std::vector has a constructor that takes two iterators. You can use that:
std::string str = "hello";
std::vector<char> data(str.begin(), str.end());
If you already have a vector and want to add the characters at the end, you need a back inserter:
std::string str = "hello";
std::vector<char> data = /* ... */;
std::copy(str.begin(), str.end(), std::back_inserter(data));