Update
With biblatex-ext styles, things are a little bit easier since you can use their cite delimiter feature.
\documentclass[british]{article}
\usepackage[T1]{fontenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[backend=biber, style=ext-numeric]{biblatex}
\DeclareOuterCiteDelims{parencite}{\bibopenparen}{\bibcloseparen}
\DeclareOuterCiteDelimsAlias{cite}{parencite}
\DeclareInnerCiteDelims{textcite}{\bibopenparen}{\bibcloseparen}
\DeclareFieldFormat{labelnumberwidth}{\mkbibparens{#1}}
\DeclareFieldFormat{shorthandwidth}{\mkbibparens{#1}}
\addbibresource{biblatex-examples.bib}
\begin{document}
Lorem \autocite{sigfridsson}
Lorem \autocites{sigfridsson}{worman}
Lorem \cite{sigfridsson}
\printbibliography
\end{document}
Without biblate-ext
With
\DeclareFieldFormat{labelnumberwidth}{\mkbibparens{#1}}
\DeclareFieldFormat{shorthandwidth}{\mkbibparens{#1}}
you get round brackets in the bibliography, for citations you need to copy the definitions from numeric.cbx and change \mkbibbrackets into \mkbibparens
\DeclareCiteCommand{\cite}[\mkbibparens]
{\usebibmacro{prenote}}
{\usebibmacro{citeindex}%
\usebibmacro{cite}}
{\multicitedelim}
{\usebibmacro{postnote}}
\DeclareMultiCiteCommand{\cites}[\mkbibparens]{\cite}{\multicitedelim}
\DeclareCiteCommand{\parencite}[\mkbibparens]
{\usebibmacro{prenote}}
{\usebibmacro{citeindex}%
\usebibmacro{cite}}
{\multicitedelim}
{\usebibmacro{postnote}}
\DeclareMultiCiteCommand{\parencites}[\mkbibparens]{\parencite}{\multicitedelim}
More radical is
\renewrobustcmd{\mkbibbrackets}{\mkbibparens}
or even
\let\bibopenbracket\bibopenparen
\let\bibclosebracket\bibcloseparen
where all square brackets are replaced by round brackets. This can lead to problems if you do want square brackets in other places in your citations/bibliography.
Note that you will need more intricate tricks for some of the more advanced numeric-derived styles and \textcite.
\mkbibracketswill now always come out as\mkbibparens, not only the citation/bibliography label brackets). – moewe Nov 26 '16 at 15:00numericstyles? It would be nice if there was something likecsquoteswhich could flip inner and outer brackets in the same way as inner and outer quotes. – cfr Nov 26 '16 at 17:22labelnumberwidthfield format, that would be OK, but the problem really is that one has to delve into the.cbxfiles, modify some\DeclareCiteCommands and even some bibmacros for\textcite. Maybe we should try and make that easier in the core... – moewe Nov 27 '16 at 07:18numeric-compstyle. – mmj Nov 27 '16 at 14:33