Is it possible to set a text file to UTF-16?

From the comments it seems your console correctly understands Unicode, and the issue is only with file output.

Here's how to write a text file in UTF-16LE. Just tested in MSVC 2019 and it works.

#include <string>
#include <fstream>
#include <iostream>
#include <codecvt>
#include <locale>

int main() {
    std::wstring text = L"test тест 試験.";
    std::wofstream myfile("test.txt", std::ios::binary);
    std::locale loc(std::locale::classic(), new std::codecvt_utf16<wchar_t, 0x10ffff, std::little_endian>);
    myfile.imbue(loc);
    myfile << wchar_t(0xFEFF) /* UCS2-LE BOM */;
    myfile << text << "\n";
    myfile.close();
}

You must use std::ios::binary mode for output under Windows, otherwise \n will break it by expanding to \r\n, ending up emitting 3 bytes instead of 2.

You don't have to write the BOM at the beginning, but having one greatly simplifies opening the file using the correct encoding in text editors.

Unfortunately, std::codecvt_utf16 is deprecated since C++17 with no replacement (yes, Unicode support in C++ is that bad).

Expanding my answer to your last question, here's a C library solution for writing the file. I saved the source as UTF-8 and compiled with Microsoft "cl /EHsc /W4 /utf-8 test.cpp".

#include <fcntl.h>
#include <io.h>
#include <string>
#include <iostream>

using namespace std;

int main()
{
    // Declare console I/O that works with Unicode.
    _setmode(_fileno(stdout),  _O_U16TEXT);
    _setmode(_fileno(stdin), _O_WTEXT);

    // Send a string to the console to verify stdout works with wide strings.
    wstring s = L"こんにちは, 世界!\nHello, World!";
    wcout << s << endl;

    // Read an input string.  I used an IME to enter Chinese.
    // Verify the stdin works...
    wstring test;
    getline(wcin, test);

    // Write it back out to stdout...
    wcout << test << endl;

    // Write it to a file as UTF-16.
    FILE *dest = fopen("out.txt", "w, ccs=UTF-16LE");
    fwprintf(dest, L"%s", test.c_str());
    return 0;
}

Output (console):

C:\>test
こんにちは, 世界!
Hello, World!
你好，马克！
你好，马克！

C:\>type out.txt
你好，马克！

Hex dump of the file content showing UTF-16LE w/ BOM encoding:

ff fe 60 4f 7d 59 0c ff 6c 9a 4b 51 01 ff

Sadly handling encoding in standard C++ is not very handy. On Posix systems single byte streams are working better, on Windows wchar_t streams are more handy.

To handle file encoding you need to set std::locale on stream using imbue.

Note that boost extends locale functionality, so it may turn out that you will have to use it to make it work.

Usually it is recommended to use system locale:

// set global locale so wcin is able to read data properly
std::locale::global(std::locale{""});

std::wstring filename;
std::wstring text;
filename = "path";
wofstream myfile;

// if you need some specific text encoding check which one your system supports
// it may be something like "C.UTF-16"
myfile.imbue(std::locale{""});
myfile.open(filename, ios::app);
getline(wcin, text);
myfile << text << endl;
wcin.get();