Biblatex \textcite using a superscript reference number

I think this will do the job: it's largely a matter of copying the definitions pertinent to \supercite into the commands that define \textcite. Please note that I have "hardwired" this, in other words it will not adapt automatically to changes in "autocite", so if you stopped using "autocite=superscript" you would need to delete the redefinitions too.

Also, as with other superscript references, pre- and postnotes are not printed, but a warning is written to the log.

\documentclass{report}

\usepackage[backend=bibtex8,autocite = superscript]{biblatex}
\usepackage{filecontents}

\begin{filecontents}{ABib.bib}
@article {article1,
 AUTHOR = {Author, A. N.},
 TITLE = {A sample paper},
 JOURNAL = {Sample journal},
 VOLUME = {1},
 YEAR = {2013},
 NUMBER = {1},
 PAGES = {1--2}}
\end{filecontents}

\addbibresource{ABib.bib}

\makeatletter
\renewbibmacro*{textcite}{%
  \iffieldequals{namehash}{\cbx@lasthash}
    {\mkbibsuperscript{\supercitedelim}}
    {\cbx@tempa
     \ifnameundef{labelname}
       {\printfield[citetitle]{labeltitle}}
       {\printnames{labelname}}}%
  \ifnumequal{\value{citecount}}{1}
    {}
    {}%
  \mkbibsuperscript{\usebibmacro{cite}}%
  \savefield{namehash}{\cbx@lasthash}%
  \gdef\cbx@tempa{\addspace\multicitedelim}}%

\DeclareCiteCommand{\textcite}
  {\let\cbx@tempa=\empty
   \undef\cbx@lasthash
   \iffieldundef{prenote}
     {}
     {\BibliographyWarning{Ignoring prenote argument}}%
   \iffieldundef{postnote}
     {}
     {\BibliographyWarning{Ignoring postnote argument}}}
  {\usebibmacro{citeindex}%
   \usebibmacro{textcite}}
  {}
  {}
\makeatother

\begin{document}
Someone saw something \autocite{article1}.

\textcite{article1} saw something.
\end{document}

Producing:

Another easier possibility if using the natbib and biber options in the biblatex package is this:

\usepackage[
    backend=biber,
    style=chem-acs,
    sortlocale=de_DE,
    natbib=true,
    url=false, 
    doi=true,
    eprint=true,
    autocite=superscript
]{biblatex}
\newcommand{\authorcite}[1]{\citeauthor{#1}\,\supercite{#1}}


\authorcite{CitationKey} 

will result in Author1 and Author^1