Yes you can dedicate a HBA to a VM so that it can access it directly but it is dedicated to that VM so cannot be shared with any other VM or used by the hypervisor. You need to use Directpath I/O. Select the ESXi host the VM is running on, on the Configuration tab under hardware select Advanced Settings, click Configure Passthrough to configure the HBA for DirectPath I/O. You can then add that HBA to your VM as a PCI device. When the tape drive is zoned up to that HBA your VM should be able to see it.
Of course as the HBA is in that ESXi host and HBAs in other hosts will have different WWN then you cannot vMotion the VM between hosts.