How to convert a RawArray of bytes to ByteArray?

At present there is no way to do this from top level, since there is no interface to the internal function that converts a rank-1 RawArray of bytes into a ByteArray.

However, as already pointed out, it's possible to take advantage of LibraryLink which will do a conversion given an MRawArray on the C side and a "ByteArray" return type, for example

Needs["CCompilerDriver`"]

src = "
  #include \"WolframLibrary.h\"
  #include \"WolframRawArrayLibrary.h\"

  DLLEXPORT mint WolframLibrary_getVersion() {
    return WolframLibraryVersion;
  }

  DLLEXPORT int WolframLibrary_initialize( WolframLibraryData libData) {
    return 0;
  }

  DLLEXPORT void WolframLibrary_uninitialize( WolframLibraryData libData) {
    return;
  }

  DLLEXPORT int mrawarray_to_bytearray( WolframLibraryData libData, 
    mint Argc, MArgument *Args, MArgument Res) {

    WolframRawArrayLibrary_Functions rawFuns = libData->rawarrayLibraryFunctions;
    MRawArray ra;
    mint rank;
    rawarray_t type;

    if (Argc != 1) return LIBRARY_FUNCTION_ERROR;
    ra = MArgument_getMRawArray(Args[0]);

    type = rawFuns->MRawArray_getType(ra);
    rank = rawFuns->MRawArray_getRank(ra);

    if (rank == 1 && type == MRawArray_Type_Ubit8) {
      MArgument_setMRawArray(Res, ra);
      return LIBRARY_NO_ERROR;
    } 
    return LIBRARY_FUNCTION_ERROR;

  }";

lib = CreateLibrary[src, "toByteArray"];

toByteArray = LibraryFunctionLoad[lib, 
  "mrawarray_to_bytearray", {"RawArray"}, "ByteArray"];

toByteArray[RawArray["Byte", {1, 2, 3, 4}]]

(* ByteArray["AQIDBA=="] *)

The new in M12 function NumericArray is essentially the documented version of the undocumented RawArray. The conversions between ByteArray and NumericArray are straightforward:

ba = ByteArray[{1,2,3,4}];
ba //InputForm

ByteArray["AQIDBA=="]

Conversion to a NumericArray:

na = NumericArray[ba, "Byte"];
na //InputForm

NumericArray[{1, 2, 3, 4}, "UnsignedInteger8"]

Conversion back to a ByteArray:

ba === ByteArray @ na

True

Note that your RawArray syntax is still supported, but it now constructs a NumericArray object instead:

RawArray["Byte", ba] //InputForm

NumericArray[{1, 2, 3, 4}, "UnsignedInteger8"]