The KDE project has a dedicated SVN client, built to work integrated with the rest of the desktop. These guides present the use of KDESVN for common Subversion tasks. Since the primary method of interaction with KDESVN is through the right-click menu in Dolphin, it can be considered an equivalent to Windows' TortoiseSVN.
KDESVN is available from most major distributions with KDE. In most cases, it is simply called kdesvn.