Hi there,
This is possible without dedicating a network adapter to a VM. Basically you can put either the vSwitch or a PortGroup into promiscuous mode and then start your capture. KB link here on what is required: VMware KB: Configuring promiscuous mode on a virtual switch or portgroup
Another option depending on your licensing level is to use "Port Mirroring" - this is the same as what you could do on a physical switch. Here is some information around this option: VMware vSphere 5.1
If however you are dead keen to still pass a physical adapter directly to a VM then what you are looking to enable is "DirectPath I/O" - there are a bunch of caveats around using this like cannot vMotion (unless using Cisco UCS), no snapshots, no suspend and resume, etc. plus your hardware needs to have VT-d. Here is some documentation around this if interested: VMware KB: Configuring VMDirectPath I/O pass-through devices on a VMware ESX or VMware ESXi host. NOTE: Some hardware while you can enable this feature don't offer support for having this feature enabled, i.e. HP
Kind regards.