I might be wrong, but neither doc nor docx formats are currently supported:
In[1]= $ImportFormats
Out[1]= {"3DS", "ACO", "Affymetrix", "AIFF", "ApacheLog", "ArcGRID", \
"AU", "AVI", "Base64", "BDF", "Binary", "Bit", "BMP", "Byte", "BYU", \
"BZIP2", "CDED", "Character16", "Character8", "CIF", "Complex128", \
"Complex256", "Complex64", "CSV", "CUR", "DBF", "DICOM", "DIF", \
"DIMACS", "Directory", "DOT", "DXF", "EDF", "EPS", "ExpressionML", \
"FASTA", "FITS", "FLAC", "GenBank", "GeoTIFF", "GIF", "Graph6", \
"Graphlet", "GraphML", "GRIB", "GTOPO30", "GXL", "GZIP", \
"HarwellBoeing", "HDF", "HDF5", "HTML", "ICO", "ICS", "Integer128", \
"Integer16", "Integer24", "Integer32", "Integer64", "Integer8", \
"JPEG", "JPEG2000", "JSON", "JVX", "KML", "LaTeX", "LEDA", "List", \
"LWO", "MAT", "MathML", "MBOX", "MDB", "MGF", "MKV", "MMCIF", "MOL", \
"MOL2", "MPS", "MTP", "MTX", "MX", "NASACDF", "NB", "NDK", "NetCDF", \
"NEXUS", "NOFF", "OBJ", "ODS", "OFF", "Package", "Pajek", "PBM", \
"PCX", "PDB", "PDF", "PGM", "PLY", "PNG", "PNM", "PPM", "PXR", \
"QuickTime", "RawBitmap", "Real128", "Real32", "Real64", "RIB", \
"RSS", "RTF", "SCT", "SDF", "SDTS", "SDTSDEM", "SHP", "SMILES", \
"SND", "SP3", "Sparse6", "STL", "String", "SurferGrid", "SXC", \
"Table", "TAR", "TerminatedString", "Text", "TGA", "TGF", "TIFF", \
"TIGER", "TLE", "TSV", "UnsignedInteger128", "UnsignedInteger16", \
"UnsignedInteger24", "UnsignedInteger32", "UnsignedInteger64", \
"UnsignedInteger8", "USGSDEM", "UUE", "VCF", "VCS", "VTK", "WAV", \
"Wave64", "WDX", "XBM", "XHTML", "XHTMLMathML", "XLS", "XLSX", "XML", \
"XPORT", "XYZ", "ZIP"}
It might be easier to save the file in plain text format. I just checked, txt files do upload to the Wolfram Programming Cloud. Just click on the upload icon below your profile icon on the upper right.
If you then just type into the notebook:
Import["filename.txt"]
the notebook will import the text.
Marco
PS: BTW, you can also upload, e.g. a docx document, but as the format is not supported you cannot import the text.