Since you're working in an online template, you can change the .cls to suit your needs.
Overleaf's Awesome CV loads all the fonts in the fonts/ older within the project. If you don't want to use Roborto, edit lines 177-216 of awesome-cv.cls where the "configuration for fonts" are set. Specifically, the class defines the following font families:
\newfontfamily\headerfont[
Path=\@fontdir,
UprightFont=*-Regular,
ItalicFont=*-Italic,
BoldFont=*-Bold,
BoldItalicFont=*-BoldItalic,
]{Roboto}
\newfontfamily\headerfontlight[
Path=\@fontdir,
UprightFont=*-Thin,
ItalicFont=*-ThinItalic,
BoldFont=*-Medium,
BoldItalicFont=*-MediumItalic,
]{Roboto}
% Set font for footer (default is Source Sans Pro)
\newfontfamily\footerfont[
Path=\@fontdir,
UprightFont=*-Regular,
ItalicFont=*-It,
BoldFont=*-Bold
]{SourceSansPro}
% Set font for body (default is Source Sans Pro)
\newfontfamily\bodyfont[
Path=\@fontdir,
UprightFont=*-Regular,
ItalicFont=*-It,
BoldFont=*-Bold,
BoldItalicFont=*-BoldIt
]{SourceSansPro}
\newfontfamily\bodyfontlight[
Path=\@fontdir,
UprightFont=*-Light,
ItalicFont=*-LightIt,
BoldFont=*-Semibold,
BoldItalicFont=*-SemiboldIt
]{SourceSansPro}
where \@fontdir points to the fonts/ folder.
Upload a new font into the fonts/ folder and update the above. If you just want good ol' Computer Modern, you can add
\let\headerfont\rmfamily
\let\headerfontlight\rmfamily
\let\footerfont\rmfamily
\let\bodyfont\rmfamily
\let\bodyfontlight\rmfamily
just before \begin{document} in resume.tex.

Note that with a change in font there is most certainly going to be a change in layout (as can be seen by the sectional unit ending without content at the bottom of the first page).
11ptoption in the\documentclassoptional argument to12pt. – Werner Dec 27 '16 at 18:2411ptand one with12ptso I can see the difference? When I change the document class option to12pt, it changes the layout so less stuff fits on the first page (an indication that the font size/baseline skip changed). – Werner Dec 30 '16 at 01:44