The company I am trying to work for uses Hogg Robinson Group for their travel management. They are requiring me to add my credit card in order to get a relocation allowance. Are these normal procedures? The company said they will reimburse me.
This doesn't sound normal. When you ask for a credit card number, usually you are asking for it with the intent of making charges to it; I've never heard of asking for a credit card number with the intention of paying it (well, not anyone who isn't trying to scam anyway). I'd ask for more information from the company or from Hogg Robinson Group as to what exactly they plan to do with your credit card information, and why they can't, for example, send you a cheque or direct deposit the money for you.
It sounds like what they intend to happen is that any relocation expenses are initially paid by you. Then you put in an expenses claim to get the money refunded.
I haven't heard of it being done that way for relocation expenses, but it's quite normal to do travel that way.
There is reason for this.
If you've ever had a corporate credit card you will have seen in the small print that if the company doesn't pay the bill you are liable (had this happen to me leaving a multinational with expenses only approved, but not paid, and mysteriously they unapproved themselves).
Similarly, should HRG relocate you and you decide you don't really want the job, the new company doesn't want to be on the end of the bill. So HRG will charge you and as you say the new company will reimburse you.
It's not great, but it's not that unusual, but find out the schedule for repayment. You may find there is some time set in your employment contract where you forfeit the expenses if you resign and they may not actually reimburse you until that passes.
I would recommend finding out why they want the card.
Given the circumstances and the preference 1 / 2 that you provided in your comment, I would guess they use the card to cover any additional expenses at accomodation, etc that you are using as part of the relocation (for example, they will cover the hotel room, but not pay-per-view).