Charlotte Mason encouraged reading the Bible daily. She assigned large portions to be memorized and recited each school year.
This is easily imitated in our homeschools for little to no money. We have friends who have done this in an interesting way. Every family member, Mom and Dad included, memorizes their birthday chapter in Proverbs. The entire chapter! (If you were born on the 4th, Chapter 4 would be your birthday chapter -- there are 31 chapters.) It's really fun to watch our friends recite their chapters at homeschool gatherings. They don't do boring, monotone recitations, but get quite animated. Plus, they've found themselves memorizing the other Proverbs chapters almost by ismosis, because they hear their parents and siblings practicing throughout the house.
Of course, Scripture needs to be put into context and not simply memorized. This can be done as children grow older. Just as primary school children memorize their ABC's before actually reading.
An interesting aside -- St. Thomas Aquinas memorized the entire Bible while he was locked away in a castle tower for a couple of years by his parents!