Yup, there are more immigrants now than ever. However, the percentage is lower than most of the 19th century. It is much higher (double or triple depending on the year) than mid-20th century. Some would have you believe they are taking over, as per this chart on left (click to enlarge):
Note the scary red columns. However, look at what has actually happened since 2010, per the dataset I downloaded from here and graphed (chart below on right – click to enlarge):
The immigrant share of population has stabilized at 13.5%. There is certainly a valid discussion to be had about the level of immigrants our country should have, and the reasons therefore, but let’s be real about the facts, and not base policy on lies.