Yes, you can import an existing directory (with contents) into an SVN repository and use the current location as your version-controlled working copy. Go at it as follows:
Suppose your (un-versioned) project sources are in /home/user/projectx, and your repository is ready at file:///svnrepo
First, create an empty directory somewhere outside of your project tree, say, /tmp/empty
. Import that empty directory in your Subversion repository:
cd /tmp/empty
svn import . file:///svnrepo/projectx
Go into your populated project directory. Now check out the repository location you created in step 1:
cd /home/user/projectx
svn checkout file:///svnrepo/projectx .
This will add the .svn files to your populated project directory, but it will not do anything else, so your existing files are safe.
Next, add the directory with your files to the repository:
svn add *
svn commit -m 'initial commit'
Done.