The only branch of the Red Cross that I can find that is accepting donations SPECIFICALLY for Taiwan is the Hong Kong Branch:
To donate to the American Red Cross Disaster Relief Fund:
The International Red Cross also has a donation page:
(again this is unspecified Disaster Relief Donations)
Donations can also be given to:
"The most pressing needs now are providing shelter, food, and clean water for those who have had to evacuate their homes," says Hank Du, executive director for World Vision in Taiwan. "We also want to make sure the children are secure and have a safe place where they are cared for."
While World Vision is working on distributing emergency supplies to victims, The Salvation Army in Taiwan is working with the country’s military in its rescue operation. It plans to help transport people and household goods back to villages once the crisis is over, provide medium-term shelter/housing and community buildings to victims, distribute disinfectant, water and other cleaning materials and equipment to affected villages in hard-hit Tainan County, and provide sleeping bags to the growing number of refugees in emergency shelters.