Microsoft user are used to have Antivirus software on their systems.
Of course you can install Antivirus software on your Mac too. But:
Starting with 10.6 (Snow Leopard), Apple began to scan all downloads for trojans. Some people said, apple never adjusted this list. Fact is, that the number of trojans and virus released for Mac is something around 10 pieces per year. Compared to Windows, there you got something like 50 per hour.
With 10.8 Gatekeeper was introduced. Software without signature can not be installed or executed on a Mac. The user explicitly has to allow it.
With 10.9 (Maverick) the execution of Flash in Safari is done in a sandbox.
New virus types are often not recognised by Antivirus scanners for quite a while. Such a virus can install itself on every system. Even if a scanner is installed.
So the answer is yes, you can become infected on a Mac. But you also do, if a scanner is installed.
If you still want a virus scanner on your Mac, consider a next generation antivirus scanner. We like and recommend SentinelOne.