After extensive testing, the last stable version of Truecaller that supports Android 2.3.6 is (released in mid-2014). Version 6.0 and above require Android 4.0+.
Android 2.3.6 has not received a security patch since 2011. It is susceptible to modern malware and exploits. When you download an unsigned or modified APK from a random website, you could be installing a virus disguised as Truecaller. This could steal your contacts, send premium SMS messages, or hijack your data. android 2.3.6 true caller download