I don't think installing the curl package installs libcurl.so.3. The curl package provides the curl program and associated files, not the library.
For Centos, the package you need is probably called something like curl-devel.
I'm a surprised yum didn't offer to install the dependencies for you. On CentOS 5.6, the yum man page says that yum install "Is used to install the latest version of a package or group of packages while ensuring that all dependencies are satisfied". I suppose it's possible that the dependencies aren't configured correctly, but that seems unlikely for something as popular as git.
Try yum install curl-devel followed by yum install git.