One way to do this is to use CustomAction and ScriptBlock, it's not pretty, but it does work.
Add a normal Module and add this:
<CustomAction Location="ScriptLink" Sequence="SOME NUMER"
ScriptBlock=";(function(){var l=document.createElement('link');l.rel='stylesheet';l.href='PATH TO CSS';document.getElementsByTagName('head')[0].appendChild(l);})();" />
Replace SOME NUMBER and PATH TO CSS with the values you need.
Update
For actually placing the CSS file on server you could use the same Module.
<Module Name="YourModule">
<File Path="YourModule\path\css\style.css" Url="path/css/style.css" />
</Module>
You could also set Type="GhostableInLibrary"
and IgnoreIfAlreadyExists="TRUE"
but since it's a Sandboxed Solution I don't think that would matter [reference needed].