Set a Data Frame Column as the Index of R data.frame object

I assume that by "Index" you mean row names. You can assign to the row names vector:

rownames(df) <- df$Date

The index can be set while reading the data, in both pandas and R.

In pandas:

import pandas as pd
df = pd.read_csv('/mydata.csv', index_col="Date")

In R:

df <- read.csv("/mydata.csv", header=TRUE, row.names="Date")