With:
read.table(file="line.txt", na.strings = "-", 
           header=TRUE, stringsAsFactors=FALSE, fill=TRUE)
where "line.txt" the name you gave to your tab-delimited text file.
Use fill=TRUE to allow for incomplete lines, from ?read.table:
fill   logical. If TRUE then in case the rows have unequal length,
  blank fields are implicitly added
na.strings     a character vector of strings which are to be interpreted
  as NA values. Blank fields are also considered to be missing values in
  logical, integer, numeric and complex fields.
To use your sample input, instead of using file="line.txt", I am simply doing:
x <- 
read.table(text='
position    SNP rs11828013  rs7931369   rs567411332 rs184532784 rs7931583   rs555937772 rs9651750   rs9651751   rs9651752   rs73530502
71278426    rs11828013  rs11828013
71278461    rs7931369   -   rs7931369
71278482    rs567411332 -   -   rs567411332
71278519    rs184532784 -   -   -   rs184532784
71278580    rs7931583   -   1.000   -   -   rs7931583
71278733    rs555937772 -   -   -   -   -   rs555937772
71278792    rs9651750   -   1.000   -   -   1.000   -   rs9651750
71278828    rs9651751   -   1.000   -   -   1.000   -   1.000   rs9651751
71278915    rs9651752   -   1.000   -   -   1.000   -   1.000   1.000   rs9651752
71279052    rs73530502  -   0.116   -   -   0.116   -   0.116   0.116   0.116   rs73530502
',na.strings='-', header=TRUE, stringsAsFactors = FALSE, fill=TRUE)
To turn this back into a lower-triangular matrix, you can then do:
x[,1] <- NULL
rownames <- x[,1]
x <- sapply(x[,-1], as.numeric)
rownames(x) <- rownames
x
which returns the matrix:
            rs11828013 rs7931369 rs567411332 rs184532784 rs7931583 rs555937772 rs9651750 rs9651751 rs9651752 rs73530502
rs11828013          NA        NA          NA          NA        NA          NA        NA        NA        NA         NA
rs7931369           NA        NA          NA          NA        NA          NA        NA        NA        NA         NA
rs567411332         NA        NA          NA          NA        NA          NA        NA        NA        NA         NA
rs184532784         NA        NA          NA          NA        NA          NA        NA        NA        NA         NA
rs7931583           NA     1.000          NA          NA        NA          NA        NA        NA        NA         NA
rs555937772         NA        NA          NA          NA        NA          NA        NA        NA        NA         NA
rs9651750           NA     1.000          NA          NA     1.000          NA        NA        NA        NA         NA
rs9651751           NA     1.000          NA          NA     1.000          NA     1.000        NA        NA         NA
rs9651752           NA     1.000          NA          NA     1.000          NA     1.000     1.000        NA         NA
rs73530502          NA     0.116          NA          NA     0.116          NA     0.116     0.116     0.116         NA