Does it require a cable between an old and a new Android phone to import a VCF file on new phone?
You can import contacts (in .vcf format) from another phone by a number of different methods but a cable between the two phones is the least likely of all.
On my phone, contacts can be backed up and restored to and from an SD card. One could backup to the SD, pop it out, put it in the new phone and restore the contacts from there.
Alternately, there are many apps and services that use cloud storage, networks, Wifi Direct, bluetooh or NFC to port contacts from one phone to another. The Play Store is full of them.
You can also use a computer to download the 0001.VCF file from one phone and upload it to the second one.
If you would post your phone type and android version, someone might be able to give an answer more specific to that model.