This question has been getting kicked around a lot, so here are some suggestions. The original prescription was a small grease gun that was original issue as an optional factory tool for MGA. It was intended for grease, but can also be used for oil to pump into the Zerk fittings on the steering rack. The rack needs six fluid ounces of EP80W90 gear oil (same stuff you put in the differential). So you can fill the little grease gun, and pump the whole load into the steering rack, reaching in behind the radiator. For MGA Twin Cam and "Deluxe" cars the Zerk fittings will be on the bottom.

Tecalemit GB2802 grease gun. This one is from a December 31, 1958 MGA.

Moss Motors sells another "palm gun" that is ideal for this job. Plastic body with maybe 8-ounces capacity. Fill it up and pump away. I find this one tends to leak when stored, so it is a good idea to pump it down to empty when you are finished with it.

Modern aftermarket plastic oil gun.

Another suggestion is to remove one of the snubber caps on top of the rack housing, extract the spring and damper plunger, and pour the oil in that way. This will be inevitably slow, but if you have enough patience it can work.

The next suggestion is to remove one of the band clamps from the rack seal (convoluted rubber gaiter on the end), and inject oil in that way. There are various techniques here, possibly a hypodermic needle, a trigger pump oil can, or a washing soap liquid pump bottle (large stye pump).

On 09 April 2017, Mike Ellsmore in Victoria, Australia wrote: "Supercheap Autos sell an ideal oil can for this job in Oz for a few bucks".

Sweet, I like it.

There are lots of cheap plastic manual oil pumps that can screw onto a one quart or one liter oil bottle, and some will adapt to the neck of a one gallon jug. You might like to look for one that includes the little metal adapter fitting that will screw into the Zerk fitting threaded port. For more of these ideas, see Tools - TS-105D

On 3/19/2020, Bo Andersen wrote:
"I didn't have a tool at hand, but came up with this solution based on what I had in the garage. A 60 ml injection syringe. I attached a small piece of plastic tube (from the tube I use for bleeding the brakes). The tube screwed onto a tread on the syringe, and after removing the Zerk it also screwed into the zerc hole in the steering rack".
60 ml is 2-fluid ounces. You would need to do that 3 or 4 times to get 6 to 8 ounces of oil into the rack (or use a larger syringe). This would be more difficult with engine and radiator (and maybe a fan shroud) in a complete car.